The thing with Rex is that he makes bad game management decisions and simply doesn't understand how to manage his offense. He calls defensive timeouts early in the half of a game that he's trailing because he is thinking as a DC first and foremost. He doesn't understand how his offense is going to need those timeouts to put points on the board in crunch time later. He's been a head coach for what, five years and he's still doing that?
Also, it was his decision to fire Brian Schottenheimer and replace him with Tony Sparano. I know Little Schotty isn't a fan favorite offensive coordinator, but he's competent and was doing good work with a bad quarterback. Tony Sparano had never even been an offensive coordinator before when Rex decided to make that switch, and the results were predictable.
In short, you can't make Rex your head coach because he simply doesn't get what's going on on one side of the ball. You will have a very good defense with Rex as your head coach, but you will have to get very, very lucky for your offense to be anything but a disaster.