George Bush Sr. wrote in his memoirs why he didn't continue on to Baghdad at the end of the first Gulf War:
"Trying to eliminate Saddam...would have incurred incalculable human and political costs.... We would have been forced to occupy Baghdad and, in effect, rule Iraq.... There was no viable "exit strategy" we could see, violating another of our principles. Furthermore, we had been consciously trying to set a pattern for handling aggression in the post-Cold War world. Going in and occupying Iraq, thus unilaterally exceeding the United Nations' mandate, would have destroyed the precedent of international response to aggression that we hoped to establish. Had we gone the invasion route, the United States could conceivably still be an occupying power in a bitterly hostile land."
Note that at the time Saddam HAD WMDs.
When he wrote "still be an occupying power" he was writing five years after the war.
I wish the senior Bush had passed on some of his skills to his errant son.