We all know that there are many places where terrorists can find support: namely almost any place where there are Islamics and enough chaos or local autonomy to protect the terrorists. This includes parts of Pakistan, Indonesia, the drug cartel areas in South America, numerous countries in South Asia like Chechnia, etc. "Evil regimes" is a convenient substitute for the much messier and harder problem of evil areas.
The best way to fight terrorism is to directly confront terrorists wherever they are. But finding them is an even harder problem and the chaos that would result from a civil war in Iraq and neighboring areas would make that job harder.
So how do you fight terrorism in Northern Iraq? How do you confront these terrorists where they are, when your enemy runs the country?
In order to eliminate terrorist safe havens in Iraq, we will have to root out the regime and install a responsible government. This will not be easy or cheap, but it is not like we have a choice. And once Iraq is done, it's on to the next.
But after three or four iterations of this, the local thugs might come to realize that supporting terrorists is hazardous to one's health.