It would be easy enough for a player to be purely random if that was all it took. I think the tension is that piece rank makes some layouts and move strategies more equal than others and calculating the best ones for what has been uncovered so far makes the best layouts not the best layouts.

In most good full information games, the best move also depends on knowledge you don't have - a full tree of all possible game states from a position. AI playing Go or Chess can't make the best move because they don't know what it is, they're technically just guessing. There isn't any reason to think AI have more or less trouble with hidden information games.

The practical difference is how many rules a game has and how easy it is to implement the engine. Implementing a chess bot is relatively easy because the amount of state tracking required to set up a simulation is basically nothing (I think just whether the king has made a move yet or not). That makes it easier to implement than something with a lot of signals that need to be recorded. Something like DoTA or Starcraft takes serious engineering effort.