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.
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.