My comment may have been unclear. I have a vague notion of a (maybe) non-PoW method that might actually work.

I have no idea whether it is possible to prove that no non-PoW method is possible. I don't think showing that PoS is impossible (not sure if we are even there yet, but as you say, refutations of claimed PoS methods always seem reasonably easy, if tedious) is sufficient.