Considering that this is as you infer a well known fact in the area doesn't it seem somewhat unusual to assume that our leaders there are unaware let alone necessarily complicit in its fruition. I realize it may seem naive of me but somehow I just don't think it's gonna be quite as easy as for ISCI as it may look on the surface.
Our President was unaware of the Sunni/Shi'i divide in Islam until shortly before the invasion of Iraq.

If there is some secret American plan to sideline or curb ISCI, it does not appear to be working given that party's level of influence in the Iraqi government and security forces. OTOH, ISCI does have the advantage of being a relatively well-disciplined force and never having been caught trying to kill American soldiers - few factions in the Iraqi government can really make that claim, excepting the Kurds.