Is wasting electricity required?

> Perhaps the proof of work could still *use* lots of resources, but delivering some side benefit to society that a miner can't directly monetize for themselves.

Not a bad idea, in principle, but there are only so many classes of problems which are uniformly hard for computers to solve, with adjustable difficulty to account for variations in technology and computational capacity, and yet very easy for other nodes to check. The stochastic element where every potential solution has an equal chance of being valid is also desirable to ensure fairness, and any system which relies on a trusted server handing out work-packets is unworkable in terms of decentralization. So far no one has managed to come up with an alternative proof-of-work with the necessary properties.