they'd stick around. Nothing in there says they have to be this proven commodity beforehand. Jay Hill is a head coach who is winning games and nobody has any idea how he'd do at BYU. Nobody had any idea how Bronco would do. Really anyone.
IF you happen to get a coach who ends up being good AT BYU, yes it's true that maybe they jump for bigger things. And to that point, who freakin cares. Frankly that would be a great thing. BYU should be a stepping stone program, not a destination program.