And while no coach is going to make decisions based on the feelings and opinions of fans and winning cures everything, if he doesn't win with Carr, he's going to burn a lot of the fan good will that every new HC has in the bank. But, sure, winning cures all.
Fan goodwill doesn't last long either way. There will be fans incensed with any number of things done, regardless of their merits, for the duration of his tenure - so why worry?