Carr was a classic case of exactly why you don't sign another team's veteran to a giant contract.
First of all there is no way to completely separate a player's impact and contribution from their team's specific scheme, talent of other teammates, and success. Carr was a low round draft choice who played opposite a guy who was a pro bowl high round draft choice.
Then there is factor involving motivation. You've paid big bucks, huge bonus, and long term contract. It's obvious from the price tag that he's the starter, no competition is there. Additionally, the team cannot afford a backup with future starting potential so the high priced veteran has absolutely everything he wanted before he even entered the field. He may intend to play his best but you really need to be pushed to accomplish this.
Therefore, you not only get uninspired play, you have also stunted the growth of the entire squad by denying opportunity to others to compete and win the job themselves. This was a Jerry jones staple in the past and it resulted in a decade and a half of mediocrity.