Actually, it was a mistake for Bush’s father to not topple Saddam in 1991 when it would have been a lot easier and the population — including the Ba’athist regime itself — was ready to accept it.
There are accounts that, after having been defeated, when Saddam and his general staff were told that they would be permitted to retain their dictatorship, they were incredulous.
In the immediate aftermath of the 1st Gulf War, there were several uprisings amongst the population and our vaunted victorious coalition stood idly by as mass-graves were filled with men, women and children.
So when US forces came in a 2nd time a dozen years later, the local population was ambivalent about it at best. Also, terrorist groups had time to fester and grow while Saddam brutalized and neglected his own people. Hence, what was possible in victory was significantly diminished in 2003 from what it was in 1991.
When a democracy goes to war against an aggressive regime, you don’t leave it in power. In war, there are only three possible outcomes: defeat, victory or a continuation of war. [Compare the result of WW2 with that of Korea; the latter war is still ongoing and the Pyongyang regime has been a threat to world peace ever since.]
In his pursuit of international approval by subordinating American strategic objectives to despotic regimes in the Saudi Peninsula, Bush’s father — whose Presidency was a disaster in many ways — chose the third option and thus guaranteed that a war left unfinished would have to be picked up later.
And indeed, it still continues there with no end in sight. That is what happens when a war is left half-done. If you’re not going to finish a war, don’t start it in the first place.