On 21 September 2002, The Memory Hole posted an extract from an essay by George Bush Sr. and Brent Scowcroft, in which they explain why they didn't have the military push into Iraq and topple Saddam during Gulf War 1. Although there are differences between the Iraq situations in 1991 and 2002-3, Bush's key points apply to both.
But a funny thing happened. Fairly recently, Time pulled the essay off of their site. It used to be at this link, which now gives a 404 error. If you go to the table of contents for the issue in which the essay appeared (2 March 1998), "Why We Didn't Remove Saddam" is conspicuously absent.
While we hoped that popular revolt or coup would topple Saddam, neither the U.S. nor the countries of the region wished to see the breakup of the Iraqi state. We were concerned about the long-term balance of power at the head of the Gulf. 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, 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 U.N.'s mandate, would have destroyed the precedent of international response to aggression we hoped to establish. Had we gone the invasion route, the U.S. could conceivably still be an occupying power in a bitterly hostile land. It would have been a dramatically different--and perhaps barren--outcome.
snip
The Gulf War had far greater significance to the emerging post-cold war world than simply reversing Iraqi aggression and restoring Kuwait. Its magnitude and significance impelled us from the outset to extend our strategic vision beyond the crisis to the kind of precedent we should lay down for the future. From an American foreign-policymaking perspective, we sought to respond in a manner which would win broad domestic support and which could be applied universally to other crises. In international terms, we tried to establish a model for the use of force. First and foremost was the principle that aggression cannot pay. If we dealt properly with Iraq, that should go a long way toward dissuading future would-be aggressors. We also believed that the U.S. should not go it alone, that a multilateral approach was better. This was, in part, a practical matter. Mounting an effective military counter to Iraq's invasion required the backing and bases of Saudi Arabia and other Arab states.http://www.thememoryhole.org/mil/bushsr-iraq.htm