The lack of any specific provisions in the NFL-NFLPA is what gives the players this leverage. If the NFL or any owner tried to fire or suspend a player without pay over these protests, the player would file a legal challenge and would win a clear victory over it. That's pretty much been acknowledged by every lawyer who has weighed in on it. In cases of ambiguity in a labor agreement, the law will always come down on the side of the employee whose job is at risk.
The NBA went through the same thing in the 1990s. The addressed in their next collective bargaining agreement with the union.
The difference in our views may be that you are speaking in terms of “fire” and “suspend”. While I do not immediately disagree with your comments in that regard, I speak in terms of “fining” and “discipline”. {;^)