We aren't moving towards useful proof-of-work because the goal of Bitcoin is to agree on one, single chain of events. By making the calculations useful, there w

We aren't moving towards useful proof-of-work because the goal of Bitcoin is to agree on one, single chain of events. By making the calculations useful, there would be greater incentive to have competing chains, which is avoided by choosing something otherwise useless, such that an adversary has to waste work in order to promote a different main chain.