The resignation of Iraq’s prime minister presents the U.S. with an opportunity for a fresh start with an essential—if often frustrating—partner, but the Trump administration faces Baghdad’s unpredictable succession process, entrenched political interests and competition from Iran, according to U.S. officials and independent experts. During his year in office, Adil Abdul-Mahdi was widely seen in Washington as a weak leader incapable of asserting his will over a fragmented government. …