The "neoconservatives" who were the strongest cheerleaders for the U.S. military campaign in Iraq had been appointed to the Bush administration long before 9/11, and their sole focus in that administration had always been to topple Saddam Hussein and "build a nation" in Iraq. If you do some research on folks in the U.S. Defense Department like Richard Perle, Paul Wolfowitz, Douglas Feith, etc. you'll find that the only background they had at all was their endless calls for "regime change" in Iraq for the entire decade leading up to 2001. These people weren't experts on the Cold War, China, or even al-Qaeda -- they were simply big-government globalists who always saw U.S. involvement in Iraq as a key element in their "New World Order."
An internet search on the terms "al-Qaeda" and "Richard Perle," for example, would reveal a shocking lack of any documented understanding of al-Qaeda for a guy who would become a key architect in this so-called "war on terror."
To appreicate the WOT significance of Iraq, all you have to do is look at a map. Beyond Saddam's role as an opportunistic supporter of various terrorist movements, his country happens to lie at a geographic nexus in the Middle East. To "flip" Iraq from an Islamic gangster regime into a western-oriented democracy creates a wedge into the heart of radical Islam. Syria is now flanked on both sides (Israel and the new Iraq) while Iran is similarly flanked by Iraq and a newly liberated Afghanistan. Coupled with underpressure from an anti-islamic India, the hotbeds of radical Islam are surrounded and feeling under increasing pressure, as evidenced by the elevated volume of their screeching and the associated whining by their fellow-marching dupes.