This is because the NFL is not an ordinary business. It is a cartel of independent teams. Such cartels, for example OPEC, are illigal in the US since 1890 but is allowed through special acts of congress. This allows it to set rules for all teams, set TV contracts, and set pay scales without any competition.
This leads to the ability to generate profits only available to socialist organizations. For instance, excessively high payment from TV networks require excessively high fees to cable providers which are paid by all cable subscribers, even if they never watch the channel. The cartel is also able to leverage national monies to convince localities to force taxpayer to fund stadiums, even if those that are never going to use the stadiums. These monies then go into individual pockets as profits.
I have heard people saying the same about music halls, but there is certainly no national cartel of music lovers that bribe local officials, that transfers the risk of the building from a for profit organization the taxpayer.
There are other costs to society. Because the rules are set, public tax dollars can be used to train kids for the NFL through public school funds. Because salaries are set, the players, though well paid, do not have the ability to truly negotiate a contract. Recall that tech firms have gotten in trouble for this, even though the employees were generally well paid.
And of course there is a fundamental loss to a society that depends on the free market that kids are taught about fair play and rules within a socialist construct where there is in fact a rule book and powerful referees. While this is useful for a 10 year old, it is disastrous when an adult goes into a work place believing her or his life is really going to be controlled by a rule book. It kills innovation and creativity. At leas in baseball you can steal a base. The immaturity of football can be characterized by the fact that everyone got their panties in bunch over deflate gate. In the real free market world that would just be considered a necessary cost of doing business.
Which is to say that the NFL basically lives within it's own bubble. It has the ability to bribe congress, or throw enough lawyers at the problem, to bend the rules no matter what previous legislation or case law says.
And I don't think the NFL is a natural cartel, like the electric company. I think real competition, not the fake thing taught to kids by the NFL structure and games, is good. I don't think sports fans are nearly as dumb as the average sports cartel thinks they are. The current structure is merely a way to maximize profit at taxpayer expense, and to create a world where fundamental rights are infringed for the sake of the bottom line or a corporation.