They're not only going after the insurgents, but a large criminal element.

But you repeat yourself.

Seriously, many times those groups are hard to distinguish. Sadr's militia is about 800 people right now. In March it was about 10,000 - Iran funnelled about 80 million to Sadr, and he paid out many cash bonuses for poor recruits. Of course, they weren't trained very well, and not a few got killed very quickly. The survivors are now no longer attatched to Sadr, but the majority of them are still on the streets, causing trouble.

There's also the nexus between terrorist/insurgent/guerilla/whatever activity and crime. There are similar structures in both: smuggling routes, police informers, safe houses, and most of all revenue generation. Using Sadr as an example again, his thugs burned down most of the licquor shops in Basra last year, claiming them an affront to Islam. But what they've done since in set themselves up in a monopoly position.

Many mafia organizations have their roots in long-lost national liberation movements. The ideology dies, but the framework remains. Crime pays.

This is one of the thornier problems in confronting an Islamic opponent. A criminal element will easily seize upon the Jihadi theme in the Koran. Be a pirate and get your 72 virgins in Paradise! Provided your victims are kuffr.

So it's better for the US to have Muslim allies in this fight. The Iraqi bloggers you cite are among them. If they're any indication, the insurgency is not going well. Mao said guerillas must be fish in a sea of people.