You attempt to personify the regime for propaganda purposes. It was used in Germany and Japan too. The emphasis may have been conveyed through the media, but the meat and potatoes was the Fedayeen, Republican Guard and the Baath Party. What was "Shock and Awe" against? All of those.
But I don't think that we dealt with the Baathist party in the proper way after we defeated the army. We should have went after them more aggressively.