> it’s not good immersion when every character is a chatbot that can inadvertently give you story beats you shouldn’t be aware of yet or you missed some crucial bit of information but no one talks about it anymore
What you're describing isn't bad dialog, it's bad interaction design.
I think your mental model might be of a single session with zero state, and no bounds on topics of conversation outside of the character's backstory. That isn't close to how this would work. A little understanding of how the game currently operates and some imagination, and you'll see how it could be improved further without degrading gameplay.
> those games would be made popular by people breaking the LLMs in funny ways
Because making the game do funny things didn't happen with RDR2, or any other game, device, or indeed humans (there are whole genre built around making people do or say "funny" things).