It is important to remember that the NFL is not football.
Football is an extremely popular sport that generates billions.
The two are not inseparable.
Death to the NFL. Long live football.
Playing our national anthem before a professional football game is incidental to the game just as much as having some dignitary toss the first pitch before a baseball game gets underway.
Such preliminaries have zero affect in the quality of play, the amount of beer consumed and spilled in the stands, and the paychecks earned by a team's players--whether they win or lose.
Why, then, is it played and/or sung before NFL games?
Short answer: money.
(There is also a long answer which some FReepers may be able to supply.)