I'm still waiting for the example of when college football teams played without a coach.
Are you serious? There are tons of examples. You don't know the history of your own program very well. The Gophers played the 1892 season without a coach and managed to go 5-0, beating Michigan, Wisconsin, and Northwestern - all of whom had coaches. Harvard played the first 17 years of their football program without a coach and won 77.9% of their games.
Even if it happened a long time ago, it could not happen today.
Sure it could.
Would it? No. But
could it? Yes, most definitely.
Players today choose a school because of the coach far more than because of the school.
Not all do. Some choose a school because it's close to home, some choose it because it has great academics, some choose it because their girlfriend (or boyfriend) go there, some choose it because their dad is on the coaching staff, some choose it because their family member(s) went to that school, some choose it because they like the color of the uniforms, etc., etc., etc. There are dozens of different decision criteria. Sometimes the coach is the sole or almost sole criteria, sometimes it's somewhere in the middle, and sometimes it's not a factor whatsoever.
Why would they show up to play if a coach didn't want them?
Because they want to go to that school? There are thousands of students who go to every FBS college in the country, and less than 1% go there because of the football coach. Those 99% would still be going to those schools, and they would build a football team from those students, just like they used to.
If my statement is false, then Alabama would always be Alabama. Their program must have been exactly the same under Mike Shula as it is under Nick Saban or was under Bear Bryant. Ohio St. would always be Ohio St. Minnesota would always be Minnesota. It must be just pure luck that the the Gophers program went from winning national championships and Big Ten titles, to a mediocre to bad program for the last 50 years.
Please point out where I said that the quality of a coach doesn't make a team better or worse. Of course it does. You're arguing against a straw man. Saban is a fantastic coach, probably the best active football coach at any level, and Alabama football is unquestionably better for his presence. But Alabama football existed before Nick Saban was even born, and it will continue to exist long after Nick Saban is dead and gone. Most Alabama fans wouldn't even call him the best coach in their own program. The coach is not the program.
If the program is the same regardless of coach
Yeah, no one is arguing that. Again, you're making things up.
Players show up to Minnesota just because it's called Minnesota right?
Some do, yes. Not every football player in the country is on scholarship, and not every walk-on is preferred. Believe it or not, there was a time when athletic scholarships didn't exist. Could Minnesota go back to that time and field a team made up entirely of walk-ons from the general student body and play 12 games without a coach? Yes, they absolutely 100% could do that. Would they? No, of course they would not. Again, that has never been the point of contention. The point you're willfully ignoring is that a coach is not a necessary ingredient to field a football team. The quality of the coach (let alone the existence of one) is absolutely a huge factor in the quality of the program. Again, that was never in debate. The coach is not the program.