I just faced the AI in a game where they had only one non-exhausted reliever. And he was listed as "Tired" at 38%. This caused the AI to let their starter throw a 159 pitch complete game (which amazingly he won). Every reliever has options, and only a couple would be in a position to decline a minor league assignment.
While I understand that emulating real life reliever churn between AAA and the Majors might be a bit much to ask of the AI, I think a situation where the entire bullpen is exhausted merits the AI going to Triple-A for a fresh reliever or two.