Once the issue is raised the battle begins. The caliph would have to be Sunni and thus the Shia would not accept any Sunni caliph. Indeed, while the caliph may be a positive symbol for Sunni Islamists, such a caliphate would be a symbol of oppression for the Shias, that is the majority in Iran, Iraq, and Bahrain, as well as a leading factor in Lebanon and elsewhere . This situation would set off Sunni-Shia wars.
As for the Sunnis, who among them might be a legitimate candidate? Ironically, the two who have the best credentials are anti-Islamist monarchs: the kings of Morocco and of Jordan who both claim—a claim that is generally recognized—descent from Muhammad, Islam’s founder.