This would never happen, in large part because of Jones' ego, but more because for all of his bluster yesterday, Jones doesn't value a head coach. The only time that he went and hired a guy who could have been considered the best candidate for the job, period, was when he hired Bill Parcells.
Johnson was hired because Jones knew him from their time at Arkansas. Imagine if he roomed with Ken Hatfield instead of Johnson on road trips?
Switzer was hired again because Jones knew him, and also to stick it to Johnson.
Gailey was hired because he came cheap, and had no designs on fronting the organization.
Campo was hired for the same reasons as Gailey.
Parcells, though it was a great move, was hired to get the stadium referendum passed.
Phillips was hired because he allowed Jones to go back to being large and in charge after Parcells made him walk on eggshells.
Garrett was hired because Jones liked him personally, and wanted to develop his own coach, allowing him to get all the credit.
Unless there's some radical epiphany that would wipe out the last 25 years of evidence, the next hire won't be someone who is a threat to Jones' place as the organizational frontman.