I thought Iraq War I was a better example of winning in terms of achieving our goals (primarily the liberation of Kuwait), and it is no accident that like Korea it was done as part of a large multinational force. When we go it alone or with a few select allies, it doesn’t work as well - either uninvolved countries are critical of it or outright supplying the enemy. Arab countries assisted in Iraq War I to restore some semblance of the status quo (and NOT depose Saddam, seen as a stabilizing force in the region); at the time they warned us they didn’t want exactly what unfolded after Iraq War II.
Yes, technically, Iraq War I did achieve its stated goals. I think it was expected that Saddam’s regime would collapse shortly after that, but did not. That set us up for a messy decade or so of controlling Iraq with limited military action. But not nearly as messy as what followed Iraq War II.
In retrospect, as odious as Saddam was, his regime did check certain blocks. Especially providing a regional counter weight to Iran. So the countries who warned us were right on. Also very doubtful that Saddam had anything substantive to do with 9/11. The Saudis (or at least some of their factions) obviously did, but their money absolved them of responsibility.