This isn't how competition works.
To restate my point: when EA puts a game on the shelf, it must stand on its own two feet against any other game that exists. That is competition. Your purchasing preferences do not change the reality of the situation EA faces when deciding to publish a video game. Looking at the situation from EA's perspective - not yours - what part of what I am saying is incorrect?
And again, EA purchasing the exclusive rights to the NFL is not anti-competitive any more than Activision purchasing exclusive rights to the 007 franchise is. Activision holding those rights doesn't stop other companies from making story-driven shooter games, other games simply can't use James Bond or any properties from / direct references to the 007 universe (except in the instance of parody, a la all the pop culture references in a series such as Duke Nukem). Likewise, EA purchasing the rights to the NFL doesn't stop anyone else from making a football game, the non-EA company just can't use the NFL to do it (except in the instance of parody, such Mike Mexico's appearance in Blitz: The League).
On the opposite end of the spectrum, is MGM required to make the 007 license available to multiple companies for use in a video game? Of course not, 007 is their franchise they may sell the rights to it however they wish. That being established, why should the case for the NFL be any different?