NXT is fine, but my main problem with Proof of Stake is where the coins come from in the first place.
With Bitcoin, we can tell everyone that nobody printed this money out of nothing, nobody just made up fake money and then sold it for real money. Proof of work means the coins are generated and earned with work, so the cost of the work gives the coins value
How so?
The same way that mining for gold helps keep it valuable - if gold was free for anyone to pick up off the ground with little effort, then it wouldn't be worth as much. No one would pay much for it, if they could get it themselves cheaply and easily. But since it is hard to find, and takes expense and effort to get, it is more valuable. If I need or want some gold, I will pay money for it because it would cost me a lot more time, effort, and money to go and find gold in the ground and get it out.
The short answer to your question is that if someone spends $100 to mine 1btc, they don't want to sell it for less than $100. So the work and cost of mining the coins helps determine the sellers' target price of the coins. And for buyers, not many people would pay $1000 if they could mine them for less than $100. But if it only costs $1 to mine 1btc, then people can and will sell them for $2 or less. So the cost of mining is a central factor.
The long answer is that if I create a new coin and give myself a billion of them, they will probably be considered worthless to most people. Why? Because if I can make a billion of them for free, then anyone else could just as easily make a billion similar coins for themselves. People have to work for their fiat money, but no work went into my billion coins. Therefore, people will not exchange their hard-earned money for my coins which were not hard-earned.
People talk about money being "backed" by something - on the gold standard, the U.S. dollar used to be "backed" by gold. The paper money could be exchanged for gold, and that is why it had value. Now, the U.S. dollar is supposed to represent the U.S. economy; all the money in the United States is supposed to have the same value as all the goods and services produced by the United States. Since it takes work to earn the money, the money "represents" the amount of work that it took to earn it. Of course, the money is devalued when the government and the banks create more money out of nothing. They bring more money into existence without requiring any representative amount of work, or goods and services, and that empty worthless "free" money is added to the overall supply, averaging down the value of each dollar.
In that case, money still has value but the value is reduced by creating more "free" money that isn't "backed" by anything. But with a cryptocurrency, if you start off with all "free" money that is generated out of thin air, then none of it represents anything valuable and will probably be seen as worthless.
That is why most people think Bitcoin is a scam - they think it's imaginary money that someone made for free, and then people sell it as a scam to take "real" money away from people. Without Proof-of-Work, they might have a point. While they may be right about certain altcoins, they're definitely wrong about Bitcoin. Bitcoin isn't created out of thin air, which is an important concern people have when they hear about it.
What is the difference between Bitcoin and a scamcoin ICO? Bitcoin doesn't "come from nowhere". It isn't "made up for free". It costs time, equipment, investment, electricity, and work to generate bitcoins. They don't come easily, and that is one reason why they are valuable. They are also valuable because they allow use of the Bitcoin network, and the Bitcoin network is valuable because it functions well for its purposes.
When I explain Bitcoin to newcomers, I always include a few facts to address their doubts: Bitcoin isn't owned by anyone or any company. Nobody creates bitcoins for free, and nobody ever did. People use computers to run the global network, and those people get the coins in return for securing the network.
Of course, Proof-of-Stake coins make a better case in that regard. I run full Bitcoin nodes, but I've never mined so much as a share in a pool. The Bitcoin network benefits from my computer, my electricity, my internet connection, my bandwidth, and my transaction fees. But I get nothing from the Bitcoin network, even though my QT has 60 active connections and has been running uninterrupted for 3 months.
PoS coins, on the other hand, allow me and my normal computer to secure the network with a full node and get rewarded for it. The drawback is that PoS requires me to get some coins before I can participate in the network, and that setup is ripe for scams. Again, one of the most important questions is "Where do the coins come from?"
If the coins are insta-mined, then they didn't take any work or effort to get. They don't represent any real value unless the network gets big or offers something else. Some coins begin with PoW and then transition to PoS. That system has its advantages, but I think there may be more advantages to a continuing hybrid PoW and PoS at the same time. But even PoW coins can be insta-mined, ninja-mined, or involve scams in other ways, so nothing is perfect.
I think there are more possibilities in the direction of Myriad/Unitus where miners can run different algos but all work for the same blockchain, and I think it would be great to see Proof-of-Stake added to that combination.
