I remember when the US invaded Iraq(II) it was treated like a party. The media loved it, it was like a football game. And when out to eat, I saw a lot of Americans were loving it , it was entertainment. Shock and Awe, it was spectacle.
The US definitely got very good at selling wars in the last decades. I remember being fascinated with the cool videos of "surgical strikes" against Iraq in 1991. Only later I read reports that a lot of the strikes weren't exactly surgical and killed thousands of civilians.
It always irked me when people called it the Second Iraq War. From my recollections, people always referred to the war in the 90's as the Persian Gulf War and it was instigated by Iraq's invasion of Kuwait. The war in the 2000's struck me as the poorly justified invasion of another nation. While there were legitimate grievances against Iraq, they were not the types of grievances that should escalate into war.
I think it is just a colloquial numbering for clarity. That is why I do it.
The 90's war was with Iraq, that is who we were fighting against, and sometimes it is just easier to number them to differentiate from the one in the 2000's.