and you're now doing something useful with that energy you were turning into heat anyway.
Is it useful? My (limited) understanding is that most of the work is just arbitrarily difficult number guessing for the sole purpose of being throttled...
It's useful because it's useless. Different definitions of "useful" at play there. Proof of work is by design unable to do anything other than provide a probabilistic proof of energy expenditure, but such proofs are themselves useful.
Is it useful? My (limited) understanding is that most of the work is just arbitrarily difficult number guessing for the sole purpose of being throttled...