[lxgr]

People have certainly tried, but I think that these comparisons don't make any sense. What makes the "waste" of crypto stand out is a qualitative concern:

HFT uses energy as a means to an end (i.e. computation), while proof-of-work mining has an incentive structure that directly rewards energy expenditure. In other words, one is energy- (and hardware-)bound, the other isn't.

As a thought experiment: If fusion energy and self-replicating nanobots were to become viable tomorrow, how would that impact HFTs and proof-of-work mining, respectively?

[xyzzy123]

You left it unsaid but wow, PoW is a horrifying grey-goo type scenario that ends in dyson spheres and intersellar war. I had never explicitly thought that through before.