Rather the leagues are federally recognized monopoly cartels. Baseball has the broad anti-trust exemption and all four leagues have media monopoly rights under the Sports Broadcast Act of 1961. One should think of each league as a single organization rather than 29 competing teams. Owners pay a high entry fee to join the cartel. In most cases, the entry fee is heavily subsidized by the public since owners don't buy teams unless and until local government comes up with hundreds of millions of dollars.
Leagues differ in how and how much revenue they share among members.
Teams keep most home gate receipts and local broadcast money but share national broadcast money and revenues from official logos, gear, etc. The leagues also differ in how much revenue they get from each source. The licensees include companies like Reebok, Starter, Russell, Champion, Wilson, Logo Athletic and Nike. Sales are billions per year and growing. Cigarette and car companies are doing a similar gear thing.