Let me first grant that hindsight is 20/20, but I do sometimes wonder if we might have been better served going for regime change back then, while the Iraqi army was folding like a house of cards and units were surrendering to news crews.
Had we continued, I'm guessing HW would have gotten even more support than his son, probably up near 90% approval compared to the 2/3 that George had for his invasion, making it highly politically correct to invade at that time. We would have been invading as a consequence of Saddam's highly offensive behavior in Kuwait, and would have something solid to point to as a moral justification. But lets set aside the value of political correctness and emotional satisfaction and consider practical outcomes.
When GW invaded, Saddam had been beaten into compliance 10 years earlier, and was not posing a threat to even his weakest neighbors. OK he did pose threats to targeted populations of opposition within Iraq, just as Assad and other Mideast dictators. But Bush Senior had contained Saddam, not perfectly by any means, but in a way which was highly geopolitically effective, and more productive than the power vacuum and the ensuing chaos left behind by his son.
From a political approval perspective, an invasion by HW would have been more easily justified, but from a practical standpoint, not invading and forced compliance was probably a more effective way of reducing Mideast instability, making the practical outcome more effective than a more emotionally based response to our own moral outrage.
The biggest unknown for me is not knowing if we would be in this clusterfuck today if we had acted differently in either the HW Administration or the GW Administration. It's easy to say, "This could have been avoided," but no one really knows that. It might be that our ability to punish and control will never match the inertia of Mideastern culture.