Had they done so, they would have had the same problems on their hands in the 1990's as we had in the 2000's.
Bush Sr and James Baker opposed the overthrow of Hussein in Iraq for good reasons, not because of "timidity." They realized that his overthrow would be followed by sectarian and tribal strife that would probably spread beyond Iraq, and so it's better to have the secular devil you know than the Islamist devil you don't running things in Iraq. Baker and his fellow realists were proven right.
The realist school of foreign policy, represented by James Baker, Lawrence Eagleburger, Cap Weinberger, and to some extent Bush Sr, has always been far more sane and fruitful than the naive and reckless crusades for "global democracy" peddled by the neoconservatives like Wolfowitz, Ledeen, Frum, and Feith. Bush the younger's main problem in geopolitics was surrounding himself with neoconservative handlers rather than realists.
We would have ended up in a post war occupation a decade earlier.
There was no point in interfering with an Arab affair in the first place