Fallujah is a city of 300,000 people of which about 200,000 still remain in the city. Out of those 200,000 people, maybe about 1,000 are bad guys.
IMO, the president's purpose in Fallujah is not to crush the 200,000. It's to get the remaining thousand or so bad guys.
If war were brain surgery, history would be very, very different.