Yea, that's one of those things that, while true to a collection of rules intended to cover other things, would in practice be the sort of thing seen as a coup. It doesn't get more bait and switch than that. Even the hardcore lefties would be livid. Remember, people want internal consistency. If they vote for Dave, even if they don't like Dave that much, they'll in their heads try to justify having voted for him. If you then use a bunch of procedural bullshit to replace him with someone completely unrelated, that conflicts with their "I chose this guy cuz he was the right choice" position.
And if you want to make the entire center and right completely decouple from any confidence in the administration, a powerplay like that would be a speedrun strat to do it with.