If you narrow the field to two sports, one of which we've been historically bad at, the answer is going to fit what you're looking for.

Beamer is an anomaly, he was a good coach who was from southwest VA and an alumni of the school. I believe he falls outside the scope of typical coaches that ride the coaching carousel.

On the other hand VT had been a basketball graveyard, one of the 4 worst P5 programs in the country, since the mid 80s before Buzz. Saying none of our coaches left early is more an indictment of how bad our program and support has been than the coaches.

Pete Hughes is the closest example of your point, and he gladly jumped ship to a better program after a top 16 finish.