Iran wants Iraq to be as compliant as Lebanon or Syria to Iranian dominance. It isn't happening:
Senior Iraqi Shia clerics told Rohani that Iraqis would not tolerate Iranian pressure or respond well to Iranian pressure.
Actually it gets worse than that because Iraq, which Iran hoped to annex or at least turn into a compliant client state, is not cooperating. In part because Arab Shia have always disliked the Iranian (Indo-European) Shia and vice versa. Iraqi Shia get regular reports of how badly Iran still (after thousands of years) treats its Arab minority. So while the Shia dominated government of Iraq pretends to be friendly and grateful towards Iran it is becoming obvious to Iran that this is all for show and not real. Opinion polls in Iraq make it clear that most Iraqis are hostile to Iran and Iranian intentions. These suspicious attitudes are on the rise. This does not mean the Iraqis are above making some cash in somewhat questionable transactions. But becoming an appendage of Iran is not going to happen willingly no matter how much the Iranians threaten, cajole and scheme. ...
Iraqis are particularly angry at pro-Iran PMF leaders who keep talking about attacking American troops as part of a campaign to get the 5,200 American troops out of Iraq. Most Iraqis understand that without the presence of those Americans Iraqi would be even more threatened by most of their neighbors (Iran, Turkey and Saudi Arabia). Even many Iraqis who are not particularly pro-American recognize this use of American troops as a “protection force.” The Americans aren’t there to fight Iraqis but to keep the neighbors from making life difficult for an independent Iraq.
We need to stay in Iraq to secure the progress we've made--and it is a real victory despite the general failure to recognize the victory.
After all, America is still in Germany and still the Germans claim to worry that could go all Nazi on Europe. Maybe we need Nuremberg Trials 2.0.
Iraq can become a beacon of democracy and rule of law in the Middle East only if we stay involved to protect and nurture the fragile sprouts of democracy in that dangerous neighborhood made worse by revolutionary Iran.
And this help includes helping Iraq rein in the Iranian-created Iraqi militias raised to resist ISIL, some of which are basically Iranian units. The militias are in theory part of the Iraqi military and this leverage must be used to pry Iran's grip from them or disband those that continue to work for Iran.
You have to admit that Iraq is important given our repeated military involvement from the Iran-Iraq War (in the Tanker War), to the Persian Gulf War, to the post-war No-fly Zone enforcement, to the Iraq War, and to Iraq War 2.0. Presidents Reagan, Bush 41, Clinton, Bush 43, Obama, and Trump have ordered military action to secure Iraq in one way or another. Obviously it is a bipartisan interest.
Wouldn't it be better if we stay involved in peacetime Iraq rather than walk away until we have to use military power to protect our interests?
And read the rest of the Strategypage post on Iran's actions.