Why Does the National Football League Deserve Tax-Exempt Status ?

Why don't the NBA, MLB, or the NHL enjoy the same status?

The NFL has maintained (except when it's convenient for them) that it is 32 individual businesses operating in a consortium rather than one large company. That's why the individual teams are taxed. Are the other leagues set up that way, or do they use the more sensical approach of operating as one organization? (serious question; I don't know the answer)