Does the college gain anything from the activity? That something is unprofitable doesn't mean it does not involve an employment activity. And students obviously are required to do these activities, and often at a high level, to maintain their scholarships.
In this case, there are no scholarships(Ivy league does not hand out athletic scholarships). So, no student is required to do anything.
In other cases where a football player is attending High Brow University on an athletic scholarship, he would be getting paid $100K (?) per year for tuition, room, board, books, fees, etc.
How about if we eliminate ALL athletic scholarships. The schools can pay individuals to play, football, basketball(whatever) but they have to be enrolled in the school, and be academically eligible.
They pay the cost out of their pay for being employees(welcome to the real world).