It is good news that Nuri Kamal al-Maliki has decided to step down as Iraq’s prime minister. This means that, for the first time in Iraq’s modern history, there is the prospect of a peaceful transition of power, based on democratic principles and without the heavy hand of the U.S. military seeming to tip the scales to one party or group.

But don’t pop the champagne just yet. As the New York Times notes today, the new prime minister, Haider al-Abadi—like Maliki, a Shiite and member of the Dawa Party—will likely face many of the same challenges that Maliki did. Abadi will need to find a way to form an inclusive coalition government, one that protects the rights of Sunnis and appeases the Kurds’ desire for autonomy, while maintaining support from Iraqi Shiites.

This is a tall order. Many in the Shiite community that was terrorized for so long by the Sunni minority harbor deep resentment toward their former oppressors. Meanwhile, the Sunnis who held power want desperately to get it back, or at least to be able to protect themselves from reprisals. Some Sunnis are so distrustful of the central government that they’ve thrown their lot with the Islamic State in Iraq and Syria (ISIS), whose barabarism seems almost limitless. It is not clear how Abadi will bridge this trust gap.

Americans should wish Iraq’s new leader well, but policymakers should resist the urge to try to micromanage political events in Iraq. Even the appearance of U.S. influence over Abadi will undermine his legitimacy and thus could be counterproductive. Besides, it isn’t obvious that U.S. action—and only U.S. action—is essential to turning things around in Iraq. One suspects that the most vocal critics of President Obama’s Iraq policy have broader concerns. As I explain in today’s Orange County Register:

[W]hen the hawks screech that Obama isn’t doing enough, what they really worry about is that others might actually be able to do without us, or with only minimal assistance. A newly energized Kurdish militia already appears to have reversed some of ISIS’s recent gains. Syria’s Bashar al-Assad might begin rolling back ISIS fighters there. And a new government in Baghdad might finally be able to fashion a credible military force. At a minimum, even modest political reforms—or the prospect of them—could convince more Sunni Iraqis to fight against ISIS instead of for them.

Any time Iraq is in the news, Americans are reminded about those who pushed for war there in the first place. It should provide an opportunity to revisit our broader foreign policy goals. Instead, U.S. policymakers and elites still call for action without any obvious sense that they’ve learned anything.

It’s time to reconsider U.S. military intervention broadly, as well as the specific advice of those who confidently, yet incorrectly, predicted that there would be no civil war in Iraq or Libya, or who called for assisting the Syrian opposition (some members of whom are now waging war in Iraq—with U.S. weaponry no less).

And while President Obama’s approval rating goes down, including for his handling of foreign policy, it isn’t obvious that the GOP can turn this to its advantage, as Pew’s Andrew Kohut noted earlier this year. A bipartisan consensus inside Washington pushed the Iraq war, and Democrats and Republicans continue to push foolish military interventions that the public wants no part of.

People outside the Beltway bubble are seeking a real change of course, not just more of the same. If they don’t get it from those who have held power for so long, they’ll look elsewhere.