I think the case will be the same for Bitcoin. The utility of the exchanges made possible by Bitcoin will far exceed the cost of electricity used. Therefore, not having Bitcoin would be the net waste.
If there's something else each person has a finite amount of that we could count for one-person-one-vote, I can't think of it. IP addresses... much easier to get lots of them than CPUs.
I suppose it might be possible to measure CPU power at certain times. For instance, if the CPU power challenge was only run for an average of 1 minute every 10 minutes. You could still prove your total power at given times without running it all the time. I'm not sure how that could be implemented though. There's no way for a node that wasn't present at the time to know that a past chain was actually generated in a duty cycle with 9 minute breaks, not back to back.
Proof-of-work has the nice property that it can be relayed through untrusted middlemen. We don't have to worry about a chain of custody of communication. It doesn't matter who tells you a longest chain, the proof-of-work speaks for itself.