You are confusing the inability to compute a full game tree with not knowing anything at all. In fact there are many positions in chess where we can compute the full game tree. Forced mates, and tablebases of positions with 7 pieces or less. And even if we can’t compute the full tree, errors get smaller with depth.

> There isn't any reason to think AI have more or less trouble with hidden information games.

How about the fact that a child can beat the best rock paper scissors player in the world in a game, but no human can beat the best chess engine? Same thing with poker, a novice could get lucky and win a hand against the best poker player.