This is a common view among opponents of the Iraq War:
Iran has gained overwhelming influence in Iraq since the 2003 US invasion brought down Saddam Huseein.
That is incorrect if you are assuming a cause-and-effect of the defeat of Saddam leading to Iranian overwhelming influence in Iraq.
Iran had influence in Iraq because the majority Shia in Iraq under the Sunni minority dictatorship had a reason to look to Shia Iran for support against Saddam. That influence was one of the motivations for Iraq to invade Iran in 1980.
As a larger neighbor with a religious connection, Iran has long had an opportunity to make inroads in Iraq.
We had an opportunity to expand our pre-2003 zero influence inside Iraq once we destroyed the Saddam regime. And we did that. Sadly, we left in 2011 in a premature mission-accomplished moment, leaving the field open for Iran.
And it got worse. When ISIL rose up in Iraq, Iran was granted the opportunity to expand their presence and influence even more to fight the renewed jihadi threat that rose in our absence.
Oh, and in our absence the Iraqi security forces deteriorated as officer loyalty to the prime minister took priority over military competence. Hence the collapse of the Iraqi security forces in northern Iraq and their defeat in the west.
So the overthrow of a hideously brutal dictator did not give Iran an edge in Iraq any more than the defeat of Hitler's Germany enabled the USSR to gain overwhelming influence in Europe despite the Soviet armies sitting on the Elbe and the strength of Soviet-backed "Euro-communist" parties in France and Italy. The difference was that America stayed in Europe to block the USSR while America left a new and still-vulnerable Iraq open to Iranian pressure.
Still, over time the past reputation of Iran as a potential savior of fellow Shias in Iraq has evaporated:
The anti-corruption demonstrations have, since October 1st, left nearly 400 dead and over 18,000 injured. The protest is not just about corruption but also the Iranian efforts to control Iraq and exploit the corruption to do so. Protestors consider the current government crippled by politicians who are pro-Iran or have been bribed to do what Iran wants. Both the Iraqi and Iranian governments were caught by surprise at the size, ferocity and persistence of the protests. This eventually included the most senior Iraqi Shia clerics backing the protestors, which was a major embarrassment for the senior Iranian Shia clerics, who have been running Iran since the 1980s and had hoped to persuade their Iraqi colleagues to adopt the same system. The Iraqi Shia clerics considered the idea after the Sunni dictatorship and Saddam Hussein was overthrown in 2003, but gradually realized that this form of religious dictatorship wasn’t working in Iran and was definitely not going to work in Iraq. The Iraqi Shia clerics tried to explain to their Iranian peers that Iraqi Shia were eager to worship together with other Shia, including Iranians, but were generally opposed to Iranian politics or political control. A growing number of Iranian clergy understand and accept this. But the Shia clergy who still control the Iranian government refuse to accept that reality, despite the fact that a growing number of Iranians are out in the streets protesting the religious dictatorship running Iran into the ground. [emphasis added]
It took the removal of Saddam to gain a long-term advantage over Iranian influence in Iraq. Let's not blow it by walking away again and tossing aside an imperfect ally that kills jihadis every day.
