The reasons the Gulf War coalition didn't remain as an occupying force in Iraq and Kuwait include:

1. The expense of maintaining an occupying force is very high, without very good payback. Easier to hand it back to the owners, and just pay for the oil. That is the main economic reason.

2. The coalition achieved it's objectives when it "won back" Kuwait, and returned it to it's rightful dictator. The international community did not give the Gulf War coalition a mandate to remain in Kuwait or Iraq as an occupying force. That is the main political reason.

3. At the time of the Gulf War, the prospect of a post-Saddam Iraq was one too terrible to contemplate, and pretty much still is. This is not a part of the world which values democratic traditions. It's more about food, prayer, and manipulating one's family's status within the traditional hierarchy, largely through the swapping of wives and daughters with other men.