Bremer felt the need to immediately and totally ban the Baath party and totally disband the iraqi army. He wanted to show that he ... means business.
Yeah, & by doing so he proved that he's an idiot.
In a system where party membership was necessary to reach certain ranks, it's likely that most party members won't be ideologically committed to the party, or loyal to it. Ban the party, & many of them won't give a damn, & some will even be relieved that they can escape from it without losing anything.
To treat every member of such an organisation as an enemy of the new regime is extremely foolish indeed. It shows a failure to understand the nature of either the Baath party, or one-party states in general. It's extraordinary that Bremer proposed it, & the US & UK governments agreed to it (apparently, he had to get approval).
De-Baathification was necessary, but that should have meant removing ideologues, personal supporters of Hussein, & the like, not everyone in an administrative position.
Same with the army. Apart from the Republican Guard, odds are that for the most part it would have been loyal to any government that appeared to have the national interests of Iraq in mind & a commitment to keeping the country intact, & didn't discriminate against Sunnis.