What I didn't fully appreciate was the lack of hard lines between the gangs and terrorists/insurgents. I viewed the gangs as background noise to be solved after the real threats of jihadis and insurgents were smashed.
Strategypage notes the more direct role the criminals have:
The war in Iraq is notable not because it is against guerillas or terrorists, but because of the large number of armed opposition groups that are, for all intents and purposes, criminal gangs. ...
Al Qaeda and Saddam's old allies had cash and cachet that made the gangs more powerful. All they had to do was support the bombing program and attacks on cops and soldiers (local and foreign). Since many of these attacks were paid for, the gangs treated it like another bit of business, even if 90 percent of the attacks on U.S. troops failed. Their paymasters understood.
Part of the reason for the Sunnis beginning to switch sided seriously and openly is the gang problem and not just fear of the jihadis:
Most Sunni Arabs now wanted the gangs gone, and were in an appreciative mood when American troops came in and took on the outlaws.
The deal was simple. We will run the local bad guys out, killing or arresting those we catch. In return, the local tribe and clan leaders will support recruiting for the local police force, and the tribe will recognize the Shia dominated government. If that happens, then American, or Iraqi, troops will be available if the bad guys try to return and reassert control. Thus peace will return, along with economic growth and a lot less violence in the streets.
So we have the gangs to defeat, too, as a primary and not a secondary goal. A large part of this is promoting rule of law in Iraq.
This fight will be helped by the fact that we've knocked down other primary threats, of course. But the gangs are in it for the money, so when the money stops, the gangs are more likely to disappear and hope to live a quiet life than fight to the death as the jihadis and high-ranking Batthists.