Their opposition does make sense though, if you look at it through the lens of their conservatism generally, meaning they don't like things to change.
NIL, players transferring, etc. make college sports more closely resemble professional sports, and a big reason why many college football fans like college football is because "they are college kids playing for the love of the game." It interferes with the quaint idea many people still have about college football, even though the days where guys were predominately playing "for the love of their school/the game" probably ended in the 70s at the latest.
You can have every game on TV, 100k-seat stadiums, and apparel/gear galore...or you can have the game be "quaint." You can't have both. If you want the game to be quaint, then the sport would have to go back to something more closely resembling intramurals or club sports...basically, what the sport was in the 1930s.
The argument that the sport can generate hundreds of millions of dollars in revenue, and coaches/admin people can make millions from it and leave whenever they want, but players cannot make anything and cannot leave is kind of untenable at this point. It simply generates too much money, and when any enterprise generates the amount of cash college athletics does, then it is going to become more about the money. We all play our own little role in it as followers of the sport.