You’re forgetting about Title IX, which is still in place. Many universities with mediocre sports programs have opted to disband their football teams if they don’t have the money for the lesser programs. But universities just cannot cancel programs they want willy-nilly. They have to factor gender equity.
That’s why we don’t have SEC Hockey, which I think would be awesome.
Football players “identify” as women during field hockey season. Now you have a fully functioning football AND field hockey team. One of each sex. Problem solved.