My guess, because the situation where we tell a coach that the player must leave is by our choice.

As Billy noted, if the coach makes that choice, it's not my responsibility. I might, depending on how things are going and the rapport I have with the coach, suggest he send an adult to the LR.

No the rationale for requiring the player to remain on the bench is that nobody wants an angry teen running around a locker room alone. And that applies equally no matter who puts the kid there.

That said, I agree with what you've said, but it concerns enforceability, not the rationale.