This is long and I skimmed it but it would take less time to correct me if im wrong. There are coins like
https://foldingcoin.net/ that reward users for doing folding for example. The problem with proof of work like this is they are usually centralized and require a centralized set of problems that can work of proofs of work.
Now a way around the centralized nature is if you can create a molecular hashing algorithm where the hash of a string is some random protein. Then the first one to fold it wins the block. Benefits to this is you are doing 'useful' work but the downside is no one probably cares about folding that random protein.
But some people definitely care about the benefit, although only very few regular people who know about benefit.
Although you do have foldingcoin and curecoin the folding@home project does predate bitcoin by about a decade. These coins have set themselves up as a reward system for a project hat was going on for years before.
As for changing the way
BTC works, I am with @mynonce here, this would be an altcoin.
I have been seeing more and more people talking about changing the way
BTC is mined, and at this point I am beginning to put them in the file of 'people who want the magical internet money for free, because I want it'
Mining will be at a cost and not a small one at that.
-Dave
