Also a Universities goal of learning is research, not teaching, especially not undergrad teaching.
Maintaining physical health is huge, but the demographic that needs to be targeted is lower performance level that club sports. Even THOSE are quite competitive. Even the (very fit) people who participate often cease physical activity and healthy eating soon after graduation.
On the other hand, subsidizing college gym facilities does tend to reach most of the student body. Required athletics classes is even more effective and pays long-term dividends (if they haven't been canceled due to COVID by now). But even more-so than that, consistent physical activity for grade school and high school would be even better from a whole society perspective.