How about replacing the PoW from solving hash to solving for example Folding@Home work units instead. But it would need a central coordinator I think, which is a major cons.
While I think that would be helpful to science, I'm pretty sure it would destroy bitcoin as a currency seeing how like your example Folding@Home work units are do not have a minimum difficulty but greatly varied by my understanding. Which in turn would mean that some people would get coins very very fast while other would get them much slower. On the other hand since bitcoin is pretty much hash breaking to get data (the transactions in said coin) it might be plausible to switch it to something that improves encryption and decryption. I maybe wrong though.