Just playing a little devil's advocate here (it's Saturday night and I'm seriously bored so it's either this or a bottle of 18 year old Scotch):
So let's say they start to play the season and you have a cluster of transmittal take place from a team or even a game. (If you've ever played football you know there's a lot of spit, sweat and blood flying around.)
Now if you've ever been part of a committed unit you know that the players want to be out there with their teammates and they're going to sign whatever waivers it takes to play, BUT let's say a couple of players get really sick (despite people who want to claim healthy 20 year old guys have nothing to worry about, there are some cases of severe reaction by healthy young people to the virus).
Now the really high end plaintiff's lawyers (trust me, you don't ever remotely understand the skill set of those guys until you actually see one in the courtroom) get involved with the argument that the kids were pressured into playing and were scared they would be kicked off the team and/or lose their scholarships if they didn't play. The collateral argument being that any liability waivers the players signed were coerced by fear of retaliation and, as a result, are invalid.
Or better yet, an Alabama player gets it after the Tennessee game and it's determined that a Tennessee player was the initial carrier. Alabama player sues UT in a Tuscaloosa court with a Tuscaloosa jury (Alabama has notoriously favorable rules for plaintiff's litigation).
Very interesting liability risk for the universities.
Same reason the Chamber of Commerce is trying to get waiver of liability legislation through Congress right now with respect to both a business's employees and its customers.