The fundamental problem that needs to be solved is voting power allocation. You have a group of people that wants to use a cryptocurrency and you want to allow

The fundamental problem that needs to be solved is voting power allocation. You have a group of people that wants to use a cryptocurrency and you want to allow everyone to voice his opinion about what transaction are valid and should be recorded and which are not so that you can determine the consensus. Your first problem is to decide who gets to vote. Does everyone get to vote or do you have to participate in the system, e.g. own at least some coins in that system? Do only humans get to vote or do legal entities like banks and companies get to vote? Does everyone get the same vote or does the number of votes vary, e.g. based on the amount of coins you own? The second problem is the hard one, you want this system to be anonymous which means you can not have a directory of voters but you have to prevent voters from casting more votes than they are supposed to have. That means you have to find some proxy for voters that is ideally impossible but in practice at least hard do duplicate. On the other hand this proxy should be easy and cheap to obtain so that every voter can make use of his vote. For the example of proof of work the assumption is that every human can own and dedicate about the same amount of computing power. It is not too easy to duplicate because you have to spend money in order to buy more computing power and in turn more votes which is better than giving one vote to each username or email address which are much cheaper to duplicate. But it turned out that it does not work all to well, people can own and dedicate vastly different amounts of computing power after all so that now only a tiny fraction of all Bitcoin users make use of their vote. Everyone else now trusts the miners on the basis of aligned incentives, i.e. malice miners would destroy the trust and usefulness of Bitcoin, driving its value down, and with that undermine their mining revenue. Personally I am quite skeptical that one can find something that works well. It has to essentially proof that you are a specific human without revealing your identity and still be unforgeable. Proxys like computing power, storage space, or money are generally duplicable by investing more money, so that it seems hard to come up with a system where voting power is not concentrated on the wealthy. This is not a fundamental problem but there are certainly people that would consider this to undermine the promise of cryptocurrencies to a certain extend because the votes and therefore the power is not spread evenly among the users and so this requires some amount of trust.