Except that on both sides of the ball, if you dominate the center of the field then you have a much easier job with the rest of the game because you're making the contested area significantly smaller.
But it's never been easier to work the middle of the field because of rules put in effect to limit your ability to hit. That's part of the reason why the Patriots have been so dominant for so long because they've dominated that part of the field.
You're better off trying to lock down the sides, get to the quarterback, and force turnovers. Beyond that, it's all about having more possessions, more time, and, ultimately, more points than the opponent.