I don't think your statement is accurate. The Iraqi army did not just "melt away deciding not to fight", they literally had no capability to fight and the time

I don't think your statement is accurate. The Iraqi army did not just "melt away deciding not to fight", they literally had no capability to fight and the times they did they got a obliterated in incredibly one sided battles. Trying to then to move focus on Fallujah, an urban pacification effort while talking about national-state-level war doesn't sound right to me either.