To keep it at the open source level, I would point out that TCPs were used outside of Fallujah and in other locales where similar large-scale clearing operations occured. They were also used in OIF I during the invasion, as civilians fled population centers, to check vehicles for fleeing combatants. How well they were executed is open to debate, but their purpose seems legit.

Without getting into TTP specifics, I would just say to look at the weaknesses mentioned and think of how they can be overcome. They can be, and many units have figured out how.