First off- I don’t think Day was ever on the verge of being canned. Or even close. His winning % is among the best of all time, and the coaches, players, families love the guy.
As far as “ the program makes the coach”—I see it the opposite in this new age.
Not only do you have to know your Xs and Os and know how to recruit, develop and motivate players ( as a good coach always has had to do), you now have to be good at so many other things.
You basically have to be a CEO at these helmet schools. You have to manage what is basically free agency with the transfer portal having multiple open windows,NIL With virtually no restrictions, Meetings with the media and managing media expectations, managing the collectives and other sources for NL money, And recruiting becomes a completely different and more complex game.
As we have seen, there are many coaches out there. They just can’t handle all of that.
Don't take this as a criticism of Day. But I think the answer to the question is unknowable right now.
A guy like Urbz won everywhere. BGSU. Utah. Florida (NC). OSU (NC). You can't do that if you're not good.
A guy like Saban won in multiple locations, but his final stop was a goddamned DYNASTY of college football. You just can't do that long term if you're not good.
Somebody like a Tom Izzo can't be evaluated upon multiple coaching stops, but a multi-decade career of absolutely killing it speaks to him being one of the greats.
Right now, we just don't know. Day has never had a HC stop before OSU, so we can't evaluate him based on his resume as a head coach elsewhere. And he's only been HC of Ohio State, a historically-strong program, 6 years. Admittedly he's proven that he's not a bad or mediocre coach, because even at OSU, the cracks would have started to show in years 3-4 when Urbz recruits started falling off, and the program "culture" became his as the effect of Urbz on program culture wore off. He's so far shown an ability to keep everything humming, so that's a feather in his cap.
I think the truth will show up over the next 4 years. So far everything looks rosy. He keeps that up? He's a great coach. If it starts to slip? He's merely adequate-to-good. But in the absence of seeing him do anything with any other program, the sample size is still too small after 6 years to know.