One original reason for military parades was to make sure there were physical soldiers in numbers to match the payroll. Big multiple unit parades assured soldiers were not being shuffled from unit muster to unit muster in different uniforms.
It would seem the Iraqi Army has the traditional weakness of corrupt armies with quite a few phantom soldiers on the payroll. But even worse, the soldiers who actually do show up go months without pay while their officers put the money in their own pockets. All of the best recruits are funneled into the Shiite militias, not the regular Iraqi Army.
If we weren't able to establish an effective Iraqi Army during our occupation, I don't see any way we will be able to do it under current, less favorable, conditions. We should be backing the folks with the best track record on both military effectiveness and religious and ethnic toleration, the Kurds.