For all the "he's got to be an Ohio guy or at least a former player" discussion (while I don't disagree that those are factors to be considered) this wouldn't auto-correct the Day/Cooper problems and (while there are certainly similarities and I think we should move on from Day), in correcting the issue(s) we shouldn't just conflate his with Cooper's.
First, we need someone with the right gut and heart to bury those knobs and the ability to convey and demand that same mentality and action from the players and staff. I don't doubt that Day, at least intellectually, understands the rivalry; maybe he didn't at first, but he's clear on it the last couple of years. He just can't actualize that. He's just not who you want with you in a fight. It boils down to that. You don't have to be from Ohio to that type of guy; see, Kirby Smart as a player and how that has translated as HC when Mark Richt couldn't get it done at UGA.
Second, we have a scheme/structure dilemma. What it takes to beat tcunt is schematically different from what it takes to win the CFP. That doesn't mean that you won't have some seasons where you do both, but it takes torque to beat the Vulverines, apparently, even when they're 6-5, and it takes horsepower to win the CFB. The argument certainly could and should be made that we would've won Saturday had we actually utilized our horsepower, but that doesn't address the fundamental issue. How do you skin that cat? That's a question that isn't answered just by getting rid of Day.