top level players distinguish themselves by coming up with imperfect continuations their opponent hasn't studied

This is exactly what Magnus Carlson does. He lures opponents into known boardstates, then does something that throws every known solution out the window, where he can then improvise a win through intuition.

The Bong Cloud is a total meme, but it's an easy to understand example of Carlson's mindset.

chess players probably wouldn't care. Computers have been better than humans at that game for a while now and it literally doesn't mat

The twitter format is annoying to parse but if you reread the op and you will see that you have just paraphrased the very first thing that Musk said.

Plus, the domain of "which moves are sensible" changes in response to how players are playing the game.

I'm not taking about moves that are simply considered optimal within a metagame but moves that are not strictly bad.

If a game is solved then following the optimal strategy will always win, so making "distinguishing moves" will always result in losing the game. If the players are deliberately avoiding studying or using the known optimal strategy then the game has indeed become like checkers.

Personally I feel that once computers have surpassed humans at a game there is a je ne sais quoi that is lost and can never be regained. There will never be the same awe seeing inspired plays and innovative strategies developed once I know in the back of my head that there is a known objectively better strategy out there. Not everyone will feel that way obviously, some can ignore the elephant and some cannot.