With Islamic State nearly vanquished in Syria and Iraq, it’s time for a serious debate about the broader U.S. security strategy in the Middle East. Leaving aside the Israeli-Palestinian peace process and its unpromising near-term prospects, this debate must address the array of issues affecting American interests in the region: violent conflict, alliances, political and economic reform, and the central challenge of dealing with Iran.

The U.S. currently leads a military coalition in support of the Iraqi government and moderate...