Yes. I agree. But we NEVER had enought troops to do this securely. That is the part that we mismanaged! Or else we wouldn't be in the position that we are today. We only had enough troops to conduct a "blitzkrieg" campaign, which WE WON. The Iraqi army WAS DEFEATED! But then..... there we didnt have sufficient setup (nor popular support) to establish peace forcefuly.
Another mistake was allowing the enemy to fold back into the neighborhoods and wait to fight another day. But that's water under the bridge as they say now.
We went to get Saddam and that mission was accomplished.