I've attended talks by a major (may be a lt. colonel now) in Central Command who blames most of the problems in Iraq on Bremer. We made no attempt to call back the Iraqi Army and get them on a payroll and on our side. The only people willing to pay them were those interested in having them cause us trouble. A couple of times he needed some Iraqi troops, so he contacted the old commander and executive officer and got 85% of the unit back together within a couple of days.
If we had recalled the Iraqi military, got as many of them back into the barracks, paid them better than they were under Saddam and worried about de-Baathifying them later, they would have been available for both security and reconstruction work (and far cheaper than our contractors).
As it was, we had a bunch of armed, newly poor people with families to support. It would have been far cheaper both in money and lives to have paid them.
(No, I won't name him. One of the conditions for attending the talk was to not refer to him by name.)
Bremer’s book is very interesting. It is all about people he met with and worked with. He worked to reach out to a broad spectrum of Iraqis and bring them into leadership to create a provisional government. That should work out a lot better than military rule ever does.
If you thought our guys were vulnerable with the disbanded army, it would have been 100 times worse with "embedded" al-Qaeda getting into the Green Zone on a regular basis as officers in the Iraqi army.