So, apologies in advance for the pedantry, but I think there's a substantive point worth making here. The NFL doesn't have an all-purpose antitrust exemption; only MLB has that (for purely historical and frankly nonsensical reasons). Certain NFL activities that would pose antitrust issues ARE protected from antitrust scrutiny by specific doctrines: The Sports Broadcasting Act allows NFL teams to pool their broadcasting rights and sell them as a mandatory bundle to broadcasters, and the labor exemption to the antitrust laws allows NFL teams to form a bargaining collective when they're negotiating with the NFLPA. But beyond that, the NFL doesn't really have special protection from antitrust cases, and has been sued successfully on antitrust theories a few times over the years.
Most notably, the NFL doesn't have any kind of antitrust exemption that would shield it from liability for anticompetitive acts designed to close the market to a rival football league. Famously, after the USFL went out of business in the early 90s, they brought an antitrust suit against the NFL and won; no one remembers that because the jury awarded only $1 in damages, finding that the USFL was doomed by its own mismanagement and not anything the NFL did. There are lots of reasons why it's somewhere between difficult and impossible for a second professional football league to form, but the NFL's ability to violate the antitrust laws when competing with a rival league isn't really one of them.
