It was the caliph's prerogative to lead prayer on Fridays, yes--or, if not to lead the prayer, to be in attendance while someone he chose led the prayer. Unexplained absences--say, outside of knowing that he was off hunting or traveling or leading an army--would lead to questions about his health and rumors about stability. Leading prayer--or commissioning it in your name--was one of the key ways that the caliph demonstrated his power and legitimacy to rule.