Iraqi Prime Minister Haider al-Abadi has called on the U.S. to deepen cooperation with Baghdad under the 2008 U.S.-Iraqi Strategic Framework Agreement. That makes sense. America has expended incalculable resources in Iraq, intervening militarily four times since 1990. Iraq is worth the effort—the center of the Middle East, with almost two-thirds of the oil and gas reserves of Saudi Arabia, abundant water, an educated population and a functioning democracy. But if the U.S. doesn’t want to intervene again, assistance must be linked to maintaining a small military contingent there.

An...