In narrative games, constraints are the point

I don't think the goal is to just have the AI characters go off the rails - they're not supposed to be a thin curtain between the player and a generalized large language model.

Instead the goal would be to have the expressive INPUT of an LLM constrained to a detailed character bio/profile provided by the game's writers. This would work particularly well in interactive fiction, but could also work equally well in a game with voice recognition.

Having a game give the conventional "tree" of pre-programmed questions that can be asked of an NPC makes a player feel like they have LESS agency. Further, in games of detective fiction, it can actually spoil the sport itself by priming the player.