I vaguely remember there being a couple of altcoins that use some kind of "useful" work for their proof-of-work. The difficulty with using something like [email protected]
is that your ideal proof-of-work should be difficult to brute force, but trivial to check. The harder it is to tell who got the right answer first, the more likely you are to have the transaction record get out of sync between different parts of the network.
Also, to Tipsy Almond's point, the people doing the mining are in fact doing a service for the bitcoin network. The huge amount of garbage number-crunching that goes into mining theoretically protects the network from being controlled by any one actor, because in order to control the network, you need to provide more mining work than the rest of the network combined. The mining reward is supposed to be an incentive to keep as many people mining as possible, thereby keeping the network secure.
In short, bitcoin by nature has to be as useless and wasteful as possible.