I already gave above. NOTHING. Or 0 if translated to numbers. This is how much users will get if they increase the number of full nodes beyond the number that is necessary for the system to function.
I am waiting for a rebuttal, waiting for your numbers, which show how much we will get.

I really want to understand the "importance of full nodes". The problem is that apart from the words about importance, you have nothing else.

Let's assume that we have full nodes in the amount that is sufficient for the full operation of all users and the system. Let it be 5 thousand.
 After that, we will increase the number to 10 thousand. What will we get? The answer I came up with after much thought: NOTHING.

If you want to convince me otherwise, you'd better provide something real, preferably with numbers. Your arguments about UASF and the Chinese pools look ridiculous and unconvincing, and very similar to FUD  .

Surprisingly, as far as I know, no cryptocurrency is worried about the number of full nodes. Only Bitcoin. Maybe it's because all the excitement about it is pointless, and does not bring any benefit.

Where are these ''engineering tabulations and analysis"?  I'd like to see them.

A properly implemented SPV client is as reliable as a full node. I don't know why, but this myth about the unreliability of SPV clients is very common in the Bitcoin community. Even more surprisingly, this myth is spread by Bitcoin developers.
The question of whether to use a full node or not is primarily a question of convenience (not even reliability). Each user decides for themselves. How many users decide to launch a full node, so many of them will be.

You decided that there should be as many full nodes as possible, and you should make an effort to increase their number. However, you do not provide any figures confirming this.

If, for example, you decide to compensate the owners of full nodes at the expense of miners, this directly reduces the security of Bitcoin. This raises the question of how optimal a solution would be to increase the number of full nodes by reducing security.

  This is not a constructive or engineering approach. Any system has optimal parameter values, or an optimal range. An unlimited increase in a parameter is usually never required, and often leads to unnecessary costs, and the effect of the increase is close to zero.
 
  Therefore, it is more correct to set the goal in a different way: for Bitcoin to work reliably, the number of full nodes should not be less than a minimum level of N. Next, we need to find out the value of N, and ensure that the number of full nodes does not decrease below this level.

  Now we have ~10 thousand full nodes. It may well turn out that this is already above the minimum level and further increase does not give any profit for the entire system.

  You think that the number of full nodes should be increased. You could use the numbers to show what will improve in the system, and how much.

Correct thinking. Just by thinking about it for a while, you can understand that neither the buyer nor the seller can benefit from creating a direct channel between them.
It is profitable for the buyer to make 1 channel to a large reliable node that has channels to other large nodes. This makes it possible to use LN for purchases from any seller.
It is also profitable for the seller to make  1 thick  channel with a large node in order to receive payments from all buyers through it, and use the amount collected inside the channel for their purchases or for selling on the exchange.

Just because someone is developing a product doesn't mean that the product will be successful. All developers believe in their product, and all hope that they will be a great success. But only a few out of hundreds achieve success.  
It took me a couple of days to understand how cool Bitcoin is. But I spent about six months intermittently on LN, but I still didn't understand what the optimism of LN developers is based on. There are too many unavoidable design flaws. My experience and my intuition tell me that LN has ~1% chance of great success.

Do you draw an optimistic conclusion from each fact? The ranks of fools with money and fans with money are not so numerous.
The user doesn't need LN. The custodial service needs LN.  If your external recipient also uses a custodial service, then they don't need LN either. And two custodial services can agree among themselves and without any LN. Why would they invest heavily in a particular channel? The way banks work with each other now.

You have an interesting way to lead a discussion. First, say that it will be more realistic if the hubs earn less. But then you claim that this will not happen, because few people will risk for a small profit and pull their funds from a cold wallet to a hot wallet that is connected to the Internet, and all the keys on this computer are open .
Either fools or fans will risk their money for a profit of less than 1% per year.
If people use custodial services, they don't need LN.

What a scoundrel.

Of course I read this blog.

Look carefully at the phrase at the end:
In fact, the author of this comment just couldn't understand the article.

The article considers a different model ( in the form of a tree), because this model should give the best results. It does not state that LN will have a model in the form of a tree. And if even for the most optimal model we get bad results, then for all other models, the results will be even worse. This is a standard technique in mathematics.

I don't recall Bram Cohen's comment. Could you give a link to this comment. If in addition to the word "stupid" there are real arguments.

This is more like a real scenario. A $ 1000 channel means that you have to pay the hub $30 per year.
If you make an average of 1 transaction per day, 360 per year, then you will get an average of $30/360 - 8 cents per transaction.
If there are 10 transactions every day, then 0.8 cents. But this is unlikely. After all, if we are considering the option with a single hub, then all your counterparties must be connected to this hub.
8 cents per transaction-this is already comparable to transactions in another blockchain. For example, take dash. There are instant payments that can be made for ~10 cents per transaction. And at the same time, you don't need any centralized hub, you don't need channels, you don't need a third party to replenish the channel. The question is, what will users prefer?

If we want to objectively assess the prospects for LN, we should not look at atypical cases. They don't make the weather.
We need to see how 90% of the standard participants will behave.

For example, how will 90% of customers use LN? How will 90% of sellers use LN?

What will be 90% of the LN network nodes? Is it profitable for these 90% to keep an LN node?

Don't believe the math in the article, because the author is a big block proponent.   Funny.
Unfortunately for you, mathematics is a neutral science.

Again, an unrealistic scenario.

 I (like most users) don't get paid$ 10 many times over the course of a month. I usually only pay$10. After 10 payments, my channel  will be reset to zero. And you will need to either re-create the channel, or replenish it using a third-party service. And this is the fee for an additional  on-chain transaction.

Is it unprofitable to keep an LN node? This means that there will be few nodes, and their number will not grow. What we have now.

Unfortunately, you are assuming the most fantastic scenario.

The math of LN Economics is pretty poor.

Let's consider the most efficient option: one LN node and many end users connected to this node.  The node must invest the same amount as all users do. If the node wants to earn 3% of the profit for the year, then all users will have to pay this 3%. That is, on average, each user will pay 3% per year of the amount invested in the channel. (The average route length will be 2).

As for me, this already raises doubts about the economic viability of the LN system.

If we consider a more distributed system of LN nodes, the average route length will increase. Accordingly, the investment efficiency will decrease. In order for nodes to earn 3% a year from their invested funds, users will already have to pay 2*3% or even 3*3% of their funds in the channel. The longer the average route length, the higher the coefficient.

"Super-cheap transactions in LN" and "LN-nodes that make a profit" are mutually exclusive things.

In 2017, there was an article dedicated to this issue.
https://medium.com/@jonaldfyookball/mathematical-proof-that-the-lightning-network-cannot-be-a-decentralized-bitcoin-scaling-solution-1b8147650800

Unfortunately, it was ignored by the Bitcoin community. Partly because they couldn't understand the math in the article. But more because the conclusions made in the article were unpleasant for LN fans.

Non-mining full-nodes cannot change the protocol. This can only be done by miners.

You want to say that full-nodes can put forward a condition that blocks will be correct if it is possible to move coin without private key. And it will force the miners to change protocol ( shoot yourself in the foot).  Fantastic scenario.

Now there are approximately 10 million users and 50 thousand full-nodes. Only 0.5% of the total number of users hold a node. Despite the fact that the cost of the node is minimal. And it's not going to improve.

Let's increase the block 10 times. Expenses will increase, but not by much. To keep a node with a 10MB block, it is enough to have a 2TB hdd for 5 years. You can take the price of such a hdd and divide it by 60 months. This will be at the level of how much users are currently paying per transaction, for each transaction. But in the end, we can get a 10-fold increase in the number of transactions and about the same increase in the number of users. Even if the percentage of users holding a node decreases, for example, to 0.1%, then in total we can get 100 thousand full- nodes. Even if the number doesn't increase, we don't lose anything. Even if it decreases slightly, which is extremely unlikely, the advantages that we will get far exceed this minus. The probability that the number of full nodes will decrease to a critical level is almost 0.

But this is moving forward, instead of the ass where Bitcoin is now.
The main reason for this is small blocks. If there were big blocks, users would not even notice the hashrate drop.

So this is the main argument of developers against increasing the block.
1.Increasing the block -> increasing the cost of maintaining full nodes -> reducing the number of full-nodes- > reducing decentralization.

2. Don't increase the block - > Expenses do not increase ( saving users money ) -> the number of full-nodes does not decrease- > decentralization is not threatened.

Thanks to the Core developers, we are briskly walking along the 2nd path. Only now these same users pay from $ 2 - $ 10 fees for transactions. Excellent cost savings for users.

How can non-mining nodes change the Protocol?
Great. Nobody is against side-chain, tokens and off-chain. Develop as much as you want. We can't ban it. Just increase the block.

You decided to find fault with 100 thousand.

"the number of full-nodes should be at least 100 thousand" - this means that we must reach 100 thousand and then, in the future, this number does not fall below this mark. This is a permanent goal.

Yes, once we had 100 thousand. This is what I meant when I wrote that users were able to run 100 thousand full-nodes. I don't know what time it is now. These statements are not related to each other.

You know the name of the topic? If you think that bitcoin works normal, that 100 MB of mempul is normal, that a fee of $10 is normal, then what do you do in this topic?

If someone claims that the system doesn't work because users are damn lazy and don't want to learn, then 100%  the system is bad. 

The answer is very simple. They don't like LN.

In other words, you set a goal so that every home user can keep a full-node. But this goal leads to a impasse  in the development of Bitcoin. This means that there will be ~10 million users on blockchain and this growth will end. We are already at this impasse for the last 5 years.

Maybe we should set a real goal? For example, the number of full-nodes should be at least 100 thousand. After all, at 100 thousand full-nodes Bitcoin will remain decentralized? And then your terrible "every week a new hard drive" transforms into ~$5000 a year. If we have a billion users, how many of them can afford to maintain a full node for $10000 a year?

These "most people are damn lazy and don't want to learn" calmly figured out Bitcoin, use a Bitcoin wallet, make transactions, and launched 100 thousand full nodes.
And when it came to LN, they immediately became stupid. Maybe they don't want to use LN because it's just a shitty system.

1. You did not provide proof about a million dollars on the node. So, it looks like FUD.
2. Now no one is demanding to increase the block to 10-100GB.
3. It will be cheaper for me to keep a node with a 10MB block than to pay$ 10 per transaction.
Do not increase the 1MB block, because it will save users money - this is a BIG LIE from the Core developer.
4.The fact that the node will be held by someone else, there is nothing wrong. 99% of users work this way now. Because a non-mining node can't harm the user in any way. After all, the user has the private keys. This is in any case better than working through Coinbase.

"Do not increase the block, because this leads to centralization.  "
and
"Go to another sidechain, or tokens on another blockchain, where there will be millions of transactions, which means there will be large blocks, but this will not be centralization."     Facepalm

Just as there is no valid proof that increasing the block necessarily leads to centralization. 

But we have excellent proff that the current block size leads to centralization for users.

Millions of new users can't use the blockchain because they simply don't fit in. And to use bitcoin, they must cooperate with custodial services. They have no other option. Coinbase, with 25 million users, demonstrates this perfectly. 25 million !!! This means that half, or even more than half of users, use bitcoin through a centralized service.

Bitcoin is turning into a network of "bitcoin banks", where users trust their funds to them, and the blockchain for transfers is mainly used by"banks".

This is not true for Dash. After Dash developed ChainLock, the reliability of transactions after confirmations is already at the level of Bitcoin.

Конечно, нет. Эта рекомендуемая стоимость вычисляется на основе количества транзакций и размеров комиссий этих транзакций в мемпуле. И она все время пересчитывается.   После увеличения стоимости биткоина  эта рекомендованная комиссия просто будет меньше в сатошах.
Те, кто утверждают, что комиссии вырастут из-за увеличения стоимости биткоина, они вообще задумаются над тем, а кто же эти герои, которые будут платить эту повышенную комиссию?
Сейчас при перечислении биткоинов на сумму в 200$ в пересчете, среднестатистический пользователь еще может позволить потратить  2-5$ на комиссию. И предположим, что стоимость выросла в 10 раз. И с какого перепугу он будет тратить 20-50$ на то, чтобы отправить 200$, и считать, что это нормально.