Mr. Trump’s approach has leaned heavily on economic coercion, flattery of ideological kin and the specter of military intervention to force regional alignment. The U.S. president apparently seeks a clean network of allies purged of perceived foreign influence or anti-Trumpian defiance. This strategy has in many ways fallen short. It is difficult to project an image of an engaged hegemon when the administration’s focus is being pulled into a Middle Eastern quagmire and even more difficult when the president’s approach relies on threats and rebukes rather than a positive agenda for the region.