This crossed my mind too, especially for the PAC-12. I saw a couple of UCLA players on the news laying out their "demands". Perhaps I'm drinking a little conspiracy theory juice here, but a quick way to shut down an organization movement is to end the season before having to answer to it. Kinda silences the thunder.
Back to the liability discussion, I have heard show after show talking about how the players want to play. However, before the cancellation of the season, I heard a lot about players being unwilling to sign a waiver to play (which could be written where neglect wouldn't be covered by the waiver). That said, other than the players trying to organize at UCLA, I didn't specifically hear any players openly being against the waiver idea. Rather the talking heads and people politicizing this on the media outlets