A linear distribution curve that matches work/watt input. This modestly levels the playing field, although it simply allows existing capital to match the input/output. Satoshi style curves are both capital dependent and skewed disproportionately to the first to arrive within the tiny timeframe.

Anti-sybil attacks would be immensely beneficial. Encouragement of honest economic activity. Scaling of bandwidth and fees.

The ideal solution is a PoW that is computationally useful and desirable, BOINC, folding@home. Ethereum almost does this, but PoW algos as they exist now are anti-scale by design, where increasing computational power does not improve the network at all.

The foreseeable longevity of PoW is ungodly waste, when a world wide distributed computing network has potential far far beyond brute force hash puzzles.

Isn't it fundamentally a bootstrapping problem? A state can reasonably presume to sell a new currency in exchange for older (or foreign) currency— this is similar to issuing a bond or whatever else to raise money. And there's a guarantee of value in the sense that the state will accept the currency later on as your taxes.

The Bitcoin network/ecosystem has nothing to offer in this sense— there's no plausible reason for it to be "raising" money by direct sales, and no one owes it taxes. So the initial tokens were distributed based on the fact that they were mined by early adopters before the difficulty got to be too great. There is indeed a basic unfairness in this, but it's not obvious to me how to resolve it for future projects of this kind.