It is a not just a missionary tool. It is a way to increase engagement of alumni with the University, massively increase donations, and prop up BYU TV-- which really needs BYU Sports.

All of that will change only when people don't come to games, don't have the passion for the team that they once did, aren't motivated to donate or feel pride in their alma mater as a result.

That all won't happen for at least 30 years I don't think. There are A TON of wealthy donors whose primary expression of love and interest in BYU begins with sports. You can't lose all of them. Or put differently, I know the Church could fund BYU without them just fine, but I doubt it would want to.