No because in the past a coach on the hot seat meant a reduction of donations to the athletic department which over time would put pressure on a staff. The coach however could turn its fortunes around by example pulling out a PAC 12 or a Big 12 championship because the reduction of donor interest to the athletic department didn't direclty impact recruiting.
Think this is naive. You think every other coaching staff recruiting against embattled coaches aren't making sure every recruit knows that coaching staff is on the hot seat? You think parents and the recruits themselves can't read thew internet?
With NIL collectives required to pay players in order to atract them donors can handcuff a coaching staff by refusing to commit 5 star money, destroying the recruiting class. There is a reason the biggest public crying about NIL is coming from Alabama and Ohio State as their recruiting can go one way or another quite quickly over NIL contributions.
There is a reason for this, but I'm not sure you've hit on it. I think the reason is that Alabama and Ohio State have had recruiting advantages and been at the top of the heap for quite a while now, and this has the potential to level the playing field. What matters is no longer solely how much money goes into a weight room and player dorms; it's also how much money goes to the player. And that's a variable they can't fully control.