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From George H. W. Bush and Brent Scowcroft, A World Transformed (1998), pp.489-90:
Trying to eliminate Saddam, extending the ground war into an occupation of Iraq, would have violated our guideline about not changing objectives in midstream, engaging in "mission creep" and would have incurred incalculable human and political costs. Apprehending him was probably impossible. We had been unable to find Noriega in Panama, which we knew intimately.

We would have been forced to occupy Baghdad and, in effect, rule Iraq. The coalition would instantly have collapsed, the Arabs deserting it in anger and other allies pulling out as well. Under those circumstances, there was no viable "exit strategy" we could see, violating another of our principles. Furthermore, we had been self-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. It would have been a dramatically different--and perhaps barren--outcome.

We discussed at length the idea of forcing Saddam personally to accept the terms of Iraqi defeat at Safwan just north of the Kuwait-Iraq border--and thus the responsibility and political consequences for the humiliation of such a devastating defeat. In the end, we asked ourselves what we would do if he refused. We concluded that we would be left with two options: continue the conflict until he backed down, or retreat from our demands. The latter would have sent a disastrous signal. The former would have split our Arab colleagues from the coalition and, de facto, forced us to change our objectives.

WHY DICK CHENEY OPPOSED GOING TO BAGHDAD IN 1991 AT THE TIME OF THE GULF WAR
Dick Cheney in April 1991, then Defense Secretary, as quoted in the Slate on October 16, 2002:
If you're going to go in and try to topple Saddam Hussein, you have to go to Baghdad. Once you've got Baghdad, it's not clear what you do with it. It's not clear what kind of government you would put in place of the one that's currently there now. Is it going to be a Shia regime, a Sunni regime or a
Kurdish regime? Or one that tilts toward the Baathists, or one that tilts toward the Islamic fundamentalists? How much credibility is that government going to have if it's set up by the United States military when it's there? How long does the United States military have to stay to protect the people that sign on for that government, and what happens to it once we leave?