Some thoughts on the merits of an account tree approach:
1) The purpose is to reduce the data storage requirements to allow the network to sync / scale faster and thereby keep the network more decentralized.
2) Blockchain size and sync/time are ultimately only part of the problem, the other part of the problem is transaction volume and bandwidth. If the goal is to support 100 million users each of whom is able to run the software on their home PC / average internet connection without entirely saturating it, then you would have to limit your bandwidth to something along the lines of 1 Megabit/sec or around 100 transactions per second which would mean each user could only do about 2 transactions per month and you are only involving about 1% of the world population in this network. This network would be generating 10 GB / month or 120 GB / year in transactions. Lets assume we could prune 50% of the transactions, 1 year would be 60 GB of data.
Compare the traditional block chain to an account tree:
A) Lets assume we have an account tree where each account consists of a public key & balance and a some other relevant accounting totaling 200 bytes per account.
B) Lets also assume that the goal is for this to scale to 100 million users world wide and that each user has exactly one account. This is not viable from a privacy perspective, so you would have to assume 10 accounts per user that rotate over time.
C) The resulting database size would be 200 GB without any indexes or other data structures.
D) To create a sha256 merkle tree on these accounts would require 64 GB
E) Assume you keep 1 month of transactions on hand for the mini-chain: 10 GB
Conclusion: The account-tree chain would require ~300 GB of storage and each user would still be limited to about 2 transactions per month.
The end result is that the account tree and full-block chain system have identical support for transaction volume, with only about a 6x gain in data storage efficiency or break even with 6 years of transaction volume.
Clearly the bandwidth is the bottle neck of scalability and not the data storage. If you allow the bandwidth to scale enough to accommodate the transaction volume of VISA then everyone would require a 1 Gigabit connection to the internet at which point you are already well beyond the scale of the average individual and well into the realm of centralized financial institutions which would be logging every transaction forever anyway, the account tree system would just be extra book-keeping for these organizations which would probably maintain a separate index optimized for their queries.
A decentralized blockchain is transaction rate limited, not storage limited. If the only change you made to the blockchain was to automatically expire / invalidate any unspent output more than 12 months old you would solve the data storage problem, the dust problem, the bootstrap problem, and the lost-key problem. And you would be left with the same scalability problems as the account-tree based approach.
What I conclude is that the account tree system at most provides some benefits for medium-scale systems involving perhaps 1 million users but is entirely irrelevant once you scale to the size Bitcoin aims to achieve.
The main thing that you are not taking into consideration is the fact that we wont reach 1 billion accounts in the account tree for an extremely long time, and by then it wont be unreasonable to expect people to deal with those sorts of large data sets (presumably). Now calculate how long it would take for the bitcoin blockchain to reach 300GB at the current rate of growth. Not too long I'm willing to bet, even with good pruning.
Furthermore, each account will be much smaller than 200 bytes, it will be closer to the 54 byte example you gave on the last page. No higher than 80 bytes in the worste case. If we assume 60 bytes instead of 200 bytes per account you'll find that it's only 55 gigabytes required. Also, the mini-blockchain will probably keep 1 weeks history or less, a full month is far too long if we need to account for very large transaction rates.
EDIT: But I do agree the system is not perfect and has its limitations, like any decentralized system. The answer is multiple competing crypto-currencies as you mentioned in your last post. But I don't think we would need thousands or even hundreds of coins, if we were to use the mini-blockchain / account tree scheme for those crypto-currencies, a few dozen or so could handle the entire worlds transaction needs I believe.
USA is way behind rest of the world, e.g. Hong Kong residents can get 0.5 Gbps for $25 monthly. This is due to telcom monopolies. Google is installing 1 gigabit where it can:
http://www.huffingtonpost.com/2013/07/24/us-internet-speed_n_3645927.htmlSo the USA crashes and burns in a heap of socialism debris. Bitcoin moves to Asia where the future is.
Also as we make our way through this global financial implosion, the mainstream are going to herd with the socialism and not adopt the new technology. It is only AFTER the destruction of their financial system, after the reset they make their way to the new thing. So mostly you will see the adoption of the digital coins limited to the astute who want to jump off the Titantic:
https://bitcointalk.org/index.php?topic=279771.msg3340053#msg3340053We shouldn't have the scaling problems, because by the time the mainstream comes on board after 2033 (when mining ceases in Bitcoin), the relevant places of growth in the reset economy will have more than 1 gigabit connections.
