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.
The Arabs specifically wanted him to remain in power with clipped wings; they wouldn’t join us if toppling him was the goal.
The aftermath of Gulf War II is our shame...