This is a total crock the overwhelming majority of the soldiers were conscripted shia muslims who were forced into the military, they would simply lay down their weapons and surrender or leave the battlefield and go home. They had zero allegiance to Saddam and his army.
That left the officers who were sunni's who were nothing but yes men, because anything but being a yes man would get you executed. Officers seen as too powerful by Saddam were routinely rounded up and shot.......
It was no longer Saddam's Army by that time - It was becoming the *new* Iraqi Army - And keeping these people paid and off the streets (along with giving them a sense of purpose and responsibility for the *new* Iraq) could have helped tremendously.
The majority (vast majority) of SOF in Country early on were against the plan that was implemented to completely disband the old (defeated) Iraqi Army.