[1] https://www.ncaa.org/sports/2019/11/12/finances-of-intercoll...
One can argue that attracting scientists and teachers with high wages and expensive toys is beneficial for research and education but it's hard to see how "professional" sports teams factor into that.
AFAIK in any country outside the US university sport teams are little more than hobby clubs for students and make do with little resources. Yet professional sports seem to be fine regardless.
NFL Clubs for example should be able to build up their own youth departments and not outsource it to the public.
Why would a university need a TV-ready football stadium for thousands of spectators with commercial exploitation of players? A "field", a few stands and a hot dog booth seems enough. Go sports team.
Also, even if the programs themselves aren't profitable that doesn't mean they don't make a net profit to the college through increased admissions. Lots of college students want to go to a school where they can tailgate and watch a football game.
The NCAA also may have an incentive to say that football isn't profitable, historically they have avoided paying athletes.