Wasn't Iraq rather overshadowed by the subsequent events in Afghanistan which does have some superb movies (Kajaki, Restrepo, Korengal, Bitter Lake....).
All due respect to those movies (3 of them which appear to be documentaries) but they have not had the same cultural impact as a movie like Apocalypse Now had back in its time. It's a shame, I'd rather a director like Nolan had made a movie about Iraq or Afghanistan instead of Dunkirk, the same as Coppola had made Apocalypse Now just a couple of years after he had directed the first two Godfather movies. That way you'd be 100% certain that said film and its vision on the realities of current war would make it to almost all the cinemas around the world.
To be fair, Apocalypse Now didn't come out until 1979, four years after the war's end and twenty four years after the war's start. Though 15 years after official US involvement. So, depending on how you count it, we still have some time :)