The problem with proof-of-work is that in order to make the ledger impeachable, people need to throw real-world value into a hole.

Most folks won't do that unless there was something tangibly "in it for them".

Bitcoin answers this with the block reward - it uses the distribution mechanism to incentivize the busywork that makes the bones of Bitcoin actually function.

The unfortunate result is that a lot of people early on in the project got a lot of coins, and if Bitcoin gets wide adoption those coins will make them about as rich as a Buffet or a Helu, and with an equal capability of screwing up the market if they had cause. (User A in the Shamir paper has 2.8 million BTC -> 28 billion dollars at $10k/coin).

So then... what? If this is a troubling result of the network rules, what rules would have worked better? How do you distribute newly created BTC in a "fair" way, when an anonymous system means that Sybil shenanigans are trivial? How do you incentivize mining, except via block rewards?

I'm sincerely interested in hearing your ideas.