Why would the Rooneys, Maras, Jerry Jones and the rest let the league make the money instead of themselves?
http://espn.go.com/nfl/story/_/id/9342479/examining-nfl-tax-exempt-status-challenged-us-senator-tom-coburn
The NFL exceeds the normal tax law. Trade organizations cannot be as exclusive as the NFL is about who they allow in and 501c organizations are supposed to serve a general interest, not a private one. The NFL operates as a private club that does not exist to promote professional football, but rather the financial enhancement of its very select members. It is not much different that a country club declaring itself to be a church, in order to escape taxation, while maintaining that it is serving the purpose of a public park. The NFL operates for one purpose only, and that is to maximize the profit of its owners/members.
The normal corporate structure would be to treat the owners as share holders.
Imagine all of the car dealerships in your town getting together and forming a tax exempt organization to advertise for them, finance car loans, set prices, and receive revenue. Further, it greatly limited membership, excluding car dealerships that didn't meet the approval of the rest of the members.
Note that the NBA is not a tax-exempt organization.