Again, those schools don't have an elite program right now, or anything close to it in some cases.
Outside of the Pete Carroll era, USC hasn't been consistently good since...the 70s? And things are only going to be harder for them now.
Tennessee has been completely and utterly irrelevant since the 90s. Same for A&M.
Michigan had a good 3 year run but they are starting at a significant regression to the mean right now, especially if Harbaugh leaves. What they built was a short term solution, not a long term one. It isn't sustainable.
So if these other alums decide to start spending like OSU did this offseason (or even more), that's great and all and sure they'll buy some recruits but it isn't going to make them a contender overnight. Just ask Miami how thats going for them. You have to build a program first. That shit takes time, a lot of time. It's not something that happens overnight by throwing money at it. You need a lot of good people in leadership positions, starting with Head Coach. Mario Cristobal is a joke. Lincoln Riley just had the biggest failure of a season in recent CFB history. I don't even know who Tennessee, A&M, or Michigan's coach is.
Respectfully, I think you're fear mongering a bit here. No, OSU is not going to win every bidding war for every kid they want. That doesn't mean this is an issue or even a threat to their success whatsoever. On the contrary, if the OSU whales are willing to spend like this consistently, combined with the established program which has been elite going on 30 years now, it's going to be to OSUs benefit. They won't even need to bid the most to win recruiting battles, they'll just need to be in the ballpark. Because the kid knows OSU is going to be better for their development than fucking bum programs like Miami/Tennessee/A&M/etc.
Lastly, schools like Miami and A&M have already been throwing crazy money around since the birth of NIL. How is that going for them? Where are the wins? When can we expect their dollars to translate to wins? This is year 4 of NIL now (I think). If this is the big deal you say it is, where are the wins? Miami plays in the ACC for fucks sake, they still can't manage to crack 8 (!) wins.