Surely the logical next step here is to make this ENORMOUS BOTNET calculate something useful? I'm thinking of solving science questions, SETI, fighting cancer, or any other distributed software projects, that kind of thing?
Mining should
not do anything useful.
Being useful in some way means that it gives an edge for some miners over others, and thus increases the risk of some group controlling half the network.
For example, if scientific institutions can make a useful product by mining, it'll make this activity effectively cheaper for them, and incentivize them to control as large portion of the network as possible. If this happens, decentralization is lost.
So, contrary to intuitive thought, mining should perform utterly useless work.
That is, useless except for the purposes of securing the network.