"Proof of useful work" has been attempted for a few things, including this. None have really taken off. I don't know all the difficulties involved super well, but sibling commenter seems on point.
Many of the attempts to use folding as proof-of-work for cryptocurrency devolve to: have some central authority keep track of how much work everyone does, then hand out coins as appropriate. And if you have a central trusted authority that can issue currency arbitrarily by fiat, you have very literally just reinvented fiat currency, in which case you might as well just create a normal mysql db instead and call it a day.
I disagree. I think centralized issuance with decentralized transaction is useful, because maybe you trust centralized authority not to abuse issueance, but do not trust it not to block transaction arbitrarily.