Right now, this is what the Iraqi army looks like:
The Iraqi army now consists of about 140,000 troops. They are organized into 113 combat battalions (91 infantry battalions, 5 mechanized infantry battalions, 4 armored battalions, 1 special-duty security battalion and twelve special intervention force battalions.) The infantry and armor battalions are organized into nine divisions. There are also four special intervention force brigades (each with three battalions.)
Consider that our divisions--prior to reorganization--had ten combat battalions each. Add a few separate brigades with three each and you have 109 combat battalions in a US Army of about 480,000 troops. I focus on pre-reorganization because of the controversy over counting line units in our new UAs that I don't wish to go into here. The point is that the Iraqis have more line units than we have even though our strength is more than three times greater.
Are the critics who focus on independent operations really saying they'd rather have perhaps 40 Iraqi battalions fully capable and reliant on their own support units rather than 113 Iraqi battalions reliant for now on US units for non-combat support? If there were only 40 Iraqi combat battalions as part of an Iraqi army capable of providing that support, wouldn't we need to replace our support units with combat units to put boots in the field? Isn't it better to have Iraqis fighting and dying for their country with Americans in safer missions providing the means for Iraqis to fight for themselves?
Honestly, the critics of our war effort would really have something to complain about if we trained and organized the Iraqi army to address their complaints about "independent units." Hell, I'd complain pretty loudly about it.