I would think one likely consequence of this is that now there'll be much less to stop the various anti-occupation Iraqis getting together to fight the occupying forces and their friends. Up until now the existence of Saddam must have made that kind of thing tricky.
While he was still "at liberty", it would have been hard building unity between people who loathed Saddam, people who supported him, and those Ba'athists who might have disliked him, but had a sort of loyalty to him. And there must have been a fear that, somehow, he might make a comeback, maybe with American backing. (After all, they backed Emperor Hirohito in Japan.)