That's really a punitive move, though, right? "You're not getting it done and before you get canned, we're going to force this move on you". Seems a tough message to deliver to a coach who is just starting with you.
I agree with your other line about the AD being able to suggest it.
I hear you, but I am not a believer in forcing an assistant onto any coach. If you want to fire them, then fire them, if not just let them do their job. If they fail with the assistant you forced on them you are giving them a built in excuse.