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.

I think that this paragraph assumes a capacity for memorization that humans just don't have. My contention is that, even if chess is "solved", the variations that branch off of the "perfect game" will still be so complex that whether or not a player knows how to punish a suboptimal move from their opponent will be an open question. IMO it would just result in a new opening game playbook that everyone memorizes, and then the decision of where and when to break off from the optimal path will become the differentiator of skill.

And noted on the OP thing, I didn't read that right at all.