> 1. Most importantly, is the algorithm a good choice? Can we eliminate some work entirely? (this is what algo interviews are testing for)

Unfortunately this has turned into a cargo cult in practice. There are plenty of cases where doing more work results in better performance, because the "faster" algorithm has some pretty horrible constants in practice.

A lot of interviews turn into a pop quiz about rote memorization of obscure algorithms because "that's what Google does", rather than actually focusing on being able to reason and benchmark why an implementation is slow and what approached could be taken to fix that.