The seasons, the dates, the tournaments are all determined in large part by the conference, the Ivy League. The irony is that all these players want to be IN the Ivy League. They can be paid by doing deals under NIL - if they are marketable, get a contract.
Football and basketball aren’t all there is to the sports in the Ivy League. Plenty of students, athletes and alums like Ivy League hockey, lacrosse, crew. Last year 5 or 6 of the men’s lacrosse team started the season in the top 20. They didn’t all stay there all year, but these schools have quality teams.
But it is no problem for you or your children to choose not to go to an Ivy because you don’t like sports, or to ignor the sports if your child does attend.