Wow. I won't even attempt to answer your penetrating question other than to say that there's another layer of C2 at work here and that is the powerful Shiite clerical heirarchy. Americans tend to disregard religious actors on the COIN battlefield except when they wield explicit political decision-making power. This is a gross underestimation of the Shiite religious system of tiered religious echelons aligned with the Marja.
Your assessment that the governor is beholden to SICI (they have publicly removed the "R" for revolution but I know what you mean) indicates the religious chain of command is at work, regardless of the formal political network as recognized in the Parliament. Shia are obligated to obey the fatwas of their Marja until the Ayatollah/Hojat al Islam dies. This is 180 degrees the opposite of Sunnaism which recognizes no formal clergy heirarchy, is dependent on scholarship and consensus, and utilizes no religious chain of command. Moreover, it is religion that cements the ties between Iraq's Shia and the Iranian revolutionary council.
I share your frustration with this thorny problem and agree that there is not much external military forces can bring to bear to untangle this corruption. However the government of Iraq will have to confront the issue (as they did in Bosra) of cleric-run militias under Iranian influence without creating 'martyrs' and inflaming fanatics. One must take into account that the majority of Shia believe that we are living in the End Times just before the appearing of Imam al Mahdi, the Shiite Savior. This apocalyptic furor is instrumentalized by many clerics as explicit justification for political and military action. Few CF INTEL/IO/PSYOP planners are fluent in these dynamics and may be operating in the dark in that regard.
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