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Why isn’t there a folding coin? Productive mining and you reward the new protein folds or whatever

Because folding is too hard to verify. For a Blockchain to work it needs to be very easy to prove that the miner has actually done the work. With a folding problem it's very hard to prove the answer a miner gives is actually a solution to the problem rather than a quick guess. It's a shame!

Just make it centralized (like most cryptocurrency effectively is anyway). You would still need some checks and balances sure.

Make a token. Altruists buy the token to fund the “miners”. They may also make a profit but they buy knowing most likely they wont and it is for a good cause.

That is what gridcoin is. Unfortunately, it doesn't work.

There's Folding Coin (FLDC)

https://foldingcoin.net/

But it never took off.

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