We allowed the Madhi Army to slowly take over security and checkpoints for Sadr City, because they weren't fighting US at least until mid 2004 and they were providing security in a area were there was no significant government security forces.
You need a certain number of security forces per person to prevent gangs and organized crime from taking root. Zarqawi was basically and organized crimial on steroids who had access to weapons, money, and explosives.
How many security forces today are in Baghdad if you include Iraqi police, Iraqi Army, Americans, Badr, and Madhi? I would bet that would be around 100,000 or more. Was Allawi's Interior Minister right that 100,000 policing forces were need for Baghdad? Maybe. It could be that less would be needed if not for the Middle Eastern problem with corruption and if the insurgency wasn't already a problem.
What I do know is you need a certain number of policing forces per person to maintain order or you have problems no matter if you are talking about Chicago, NY City, or Iraq.