In fact, as you suggested later, SHA-512 is actually much less computationally expensive on 64 bit machines - it has 25% more rounds, but you can do twice the number of bytes per round.

All other things being equal (which they seldom are), you will often see a significant speed improvement with SHA-512 vs. SHA-256 on larger payloads.

Of course, I immediately tried to test this with "openssl speed" on my M1 Mac and SHA-512 is 70% slower, so I guess there's some architectural optimization there.