Because the spread offense makes a living with a high tempo game that gives the defense little time to rest. That is your own defense has little time to rest. A big 3-4 defense is typically matched with a ball control offense that gives the defense can rest. I would find it hard to match the two together.
You are correct, about the NFL anyways. It could be done in college because you have 85 scholarship athletes, plus any non-scholarship players... The NFL only allows for a 56 man roster, thus you can't substitute they way you do in college. The defense would start well, but by the fourth quarter they'd be dogged. The best defense you can hope for with such an up tempo offense in the NFL is to save money by not spending on top tier defenders, but stockpile lots of interchangeable players with lower contracts. That way you can rotate as much as possible, and hope you out score the other team...