I think if you will look around at all the coaching changes over the years you will find that QB changes are far from automatic, and the QB only changes when the current QB is some career backup who is just temporarily manning the position, or is a guy that has been given his shot and never had any success. Neither of those things apply to Dak.
The reality is even if Dak isn't the ideal guy, a new coach can't just waltz in and find someone better. It's not as easy as some fans want to imagine. Even if the team were to have a top 5 draft pick to use on a QB (which they won't), that still is far from a certainty. Somebody started a thread a few days ago that showed all the first round picks that have been used on QBs the last 10 years or so, and far and away most never reached Dak's level.
The bottom line is the future of a coach depends on how successful he is, and a coach isn't going to want to risk floundering around a few years looking for a QB. His job may not survive it.