As long as Hussein lives, the U.S. has a reasonable cover for maintaining a powerful presence in the region as a big-stick protectorate of Israel. Seems to me we want to keep him in power.
On the other hand, with the newly developed resistance we are seeing from the Royals in Saudi Arabia, it may become necessary for the U.S. to establish a series of military bases in the region which do not require permission for use from regional authorities. This might be accomplished by invading southern Iraq. Permanent bases in such a position would be strategically located on the gulf with direct access to Saudi Arabia, Iran, Iraq and Syria.
Maybe it's just a subtle difference for some people, but I don't believe they wanted to "keep him in power" -- rather, "didn't want to go after him." I think 41 would have loved to get rid of Hussein a decade ago. There was no support for such a move, and we would have been utterly vilified worldwide. Furthermore, didn't Kuwait ask us to help them? After that 'mission' was over, we were done. People love to talk right now about the sorry, ridiculous "interventionist" policies of the USA. Going after Hussein in 1991 would have been just that: sorry, ridiculous, and interventionist.