Get China out of the picture more like, after all, they've been helping Hussian recently.
True, in 1991 the allies had a chance to remove the madman, not by invading Bagdad, but at the end of the ground war two Republican Guard divisions were allowed to escape from the air power and the US and British armoured divisions.
Weeks later, when large sections of Iraq rose up against Saddam those same units brutally repressed them, and lots of civillans too. This saved Saddam's neck, it was a close run thing though.
IMHO Bush snr could not believe his luck that there were so few US casualties as the ground war progressed, so why push it?
Around the same time, the Iraqis got lucky with a SCUD shot, it killed dozens of National Guardsmen at a Saudi airbase. More of that, and increased losses from further engagements, then the yellow ribbons would be out. Not good politically for Bush.
Bush would not have needed much persuasion to disengage, Colin Powell pushed for it, he'd been against the Desert Shield operation in the first place after all.
As for 'thousands of dead since'. UN food and medical aid gets to Iraq, and goes straight to the elite and military.
Iraq is allowed to sell oil for food, it chooses not to.
But US and UK policy there is looking like diminishing returns.