Revoking their tax status or their monopoly status should not "take down the entire league". Just ask them to play by the same rules everyone else has to play by.... including Major League Baseball.... and the rules the fans have to play by.... you know... the ones sitting in the stands and the one glued to the game on TV.
You know this and I know this, but just think about the media blitzkrieg the NFL would go on to rally public outcry and the narrative that they would use to do that: "It's government vs. the private sector! They're trying to destroy our business! This is an overreach by a totalitarian government!" And while the motivation for the government's actions may make that last statement at least partially true, you and I know that it would actually be forcing the league to stand on its own legs and compete in the free market without government favors. But that's not what Goodell would would be out there telling the press, and given the anti-government sentiment that's (justifiably) popular right now, it's rather obvious whose side the public would take.