I have a conceptual problem with my view of GTO play. My understanding is that the idea of playing GTO is to be unexploitable. I understand that when playing perfect GTO, at any game, you become invincible in the long term. Nothing the opponent can do can exploit your play. However, it seems to me that the reverse is also true - i.e. it should not be possible to beat opponents in the long term by playing GTO.
For example, if you play Rock, Paper, Scissors, the perfect GTO strategy is to randomly select between the 3 choices. You can't be beat in the long term with this approach but you also can't win in the long term - any opponent strategy will result in a long term draw. If they pick paper every time then you win 33% or the time and lose 33% of the time.
So why should we aim to play GTO? How do we profit from this? Am I missing some key concept that means we win whenever our opponent makes a bad/suboptimal play in poker?
Or is the aim to learn GTO play and then learn how to diverge from it in order to exploit opponents better without risking too much bad play on our own part?
I'd really like to understand this - can anybody explain?