Agreed.

Well, they do slightly different things but I agree with your point. I think that players need to optimize more (aiming for a smaller slice of search space, with fewer possible actions), but that there's lots of useful rationality training you get from running the game that you don't get from playing.

Running a game gives you more experience working with different epistemic states. Like, nothing exists in the game-universe until you say it does so you have in your head what you know and are thinking of having happen, and what the players know. Good GMs are able to keep the two straight and change what they thought was happening, but wasn't yet revealed, behind the scenes in able to adapt. For example, if you had another ambush in an encounter but the party's already beat up you can just not have the ambush happen.

GMs also need to better predict other people's actions, agreed. And design challenges that aren't so easy as to be boring, but not so hard as to total party kill.