At the time of 9/11 and for many years before NORAD was not functioning, and even when it was functioning as designed it's mission was only to interercept an attack from Russia across the Canadian border from the North, not deep within American air space. It was not designed to function as an air patrol to take out a commercial flight taken over by suiciders.
To make that kind of change of mission might have taken an immediate change of command by the VP who was in the nation's secure command post (CP), and to make that kind of order could be made by none other than the highest command.
We were never as instantly ready for all types of air defense scenarios as some naive people assumed then or now. We were very vigilantly relaxed then, after the end of the Cold War, with a false sense of security.