For starters, we did completely dismantle the SS; and the Germans had an EXTREMELY professional army before the war that acted distinctly different from the SS, and which managed to survive Hitler - at least in part. Anyone in any sort of leadership position in Iraq's army was a Baathist - he'd done a Stalin-like purge of the Iraqi military before the first round of the Gulf War.
Leaving the set of connections and inter-relations intact would have been yet another obstacle to deal with. You may have noticed, but even as it is we've had a notable amount of trouble from infiltration into the various government agencies...imagine if we simply left them in place. Imagine also whether or not there would be any Kurd or Shia ability to trust the organizations?
We employed Nazi party members to operate the power stations and waterworks in post-War Germany. And it is my understanding that only SS totally verboten were Waffen politico types. And we quickly assembled the officer cadre into the new W. German army to counter the rise of monolithic Communism on its eastern border by having them recant oaths to Der Fuhrer and swearing to their country and constitution--something that should have been done in Iraq, IMO.