as lcampbell said, the point of mining is actually to keep and confirm legitimate transactions. Mining needs to be a 'difficult' (but otherwise useless) problem like cryptographic hashing in order to make it difficult to fake transactions. Computations which might be useful in some other way are too easy - only cryptographic hashing is 'difficult' enough to stop the fakes.

It's kind of like captchas - a seemingly pointless pain in the ass on purpose to weed out the spam.