I would think that numerous licensing issues would come in to play, especially considering the numbers of exclusive brands/contracts that are negotiated by the various teams and sporting venues to be sold at those stadiums (ie Coke, Budweiser, Farmer John, clothing, etc, etc, etc). Reference also the extensive advertising found at most if not all professional sporting venues.
I would also imagine that there are clauses written into the Collective Bargaining Agreements for the various sports that both prohibit the various leagues from imposing specific advertising (other than league negotiated clothing contracts), and also prohibit players from wearing other apparel brands as a part of their uniforms.
I seem to recall this being somewhat of an issue (perhaps in the NFL?) recently where a player(s) were fined for wearing certain brand gear which the league didn't authorize.
Tom at MSY
"The criminal ineptitude makes you furious"-Bruce Springsteen, after seeing firsthand the damage from Hurricane Katrina