Saddam Hussein was never a true US ally. In the Iran-Iraq war the US supported him after 1982 as the lesser evil in the conflict in order to prevent Iran from overrunning Iraq and spreading its influence in the Middle East (there are assertions but no proof that the US encouraged or greenlit Saddam’s invasion), something that would have severely destabilized the regional balance. That doesn’t mean that US in was actually supportive of Saddam or his goals, Kissinger’s quote of "It's a pity they both can't lose” sums up pretty well the US position.
Also, there is no straight road from 1991 to 2003. It was the later invasion of Iraq that destabilized the country and led to the rise of groups like ISIS, not the 1991 intervention in Kuwait and there is no reason to think that the intervention in Kuwait had to necessarily be followed up by an invasion of Iraq.
Allowing Saddam to annex Kuwait would not only have led to Saddam being in a controlling position over a pretty large part of the world’s oil reserve, but also to the destabilization of the Middle East as Saudi-Arabia would feel deeply threatened by Iraq and at minimum instigate an arms race in the region that would have dwarfed Saudi-Arabia post-Gulf War military expansion and possibly going nuclear as a deterrent against Iraq as the Iraqi army was a lot larger than the Saud military.
The international implication of the UN allowing Saddam to annex Iraq in direct violation of the rules of international law would also have been devastating. The UN would have proven itself an even bigger paper tiger than anything it did IOTL that cannot even enforce one of its core rules (no territorial acquisition by force) against a regional power like Iraq. Any power with territorial claims against its neighbor would take notice and wars between countries would likely again be much prevalent than IOTL today.