Mining the coin serves the benefit it does for every other coin; security, and producing a block chain around provably-fair cryptographic hashing functions. It would be better if everyone threw all their power at folding (at least for the folding project), however it would then not produce a currency. 
And what are the benefits of producing a currency? (which, like every cryptocurrency, is not backed by anything and cant get value without additional effort) Why not mine BTC and give rewards to those who are folding in an established currency that already has value instead?