I would add to your guess that since the center of attention is Baghdad they see the need to completely control it. Not too much attention gets payed to Anbar province unless Americans are dying there. Pacify Baghdad and leave Anbar for another day?
Whack-a-mole
---Pacify Baghdad and leave Anbar for another day?---
Or hunker down in Baghdad until it's time to catch the last flight out. I'd like to see an indication that someone wants to win this thing and has some kind of idea about how to do it.