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SETI@home and Folding@home at least provided intrinsic value from their computations. It'd be nice if we could have a coin based on protein folding or climate simulations or something.

There's at least one coin that does that. It's a Nano clone (not sure if clone is the right word), called Banano.

You "mine" it by joining their folding@home team, and you get banano based on how many folding@home work units you complete. It's pre-mined though, so maybe that doesn't quite fit.

There was another cryptocurrency I remember which was mildly popular years ago called Primecoin, which attempted to find a certain type of prime numbers. It's interesting, but I'm not sure if it ever provided any actual usefulness from the work performed.

I don't see any reason that a cryptocurrency couldn't be tied to something like protein folding or climate simulations. People just don't choose to do so.

How funny - you must be a little younger.

When bitcoin mining first became a thing, it felt like they'd found a way to make distributed computing (like the seti and protein folding projects) profitable.

ahh that was distributed.net