In this scenario, where you have a vet QB that has had some success, granted mostly regular season stuff, you'd probably dump the GM and coaches, hire a new GM, find a new coach and then they decide if they can with the current QB.
I mean if Harbaugh came in here, for example, and said he could absolutely win with Dak because he's going to build a ground and pound offense, heavy play action that suits/limits Dak to not airing it out 35 times a game, that might work and I'd certainly trust what Harbaugh thinks.