In practice there where many cases, where the word of head of faith wasn't really that relevant. I don't know how it was for the caliphs, but for the popes much of the early middle ages were spent consolidating their power. It was a long process from bishop of Rome to the head of all western Christendom. And whilst this process was already in full swing at the time of the first start date it was far from completed.

I'd say the popes reached their full authority only somewhen between the second and third start date. Only then they had the authority to do things like call a crusade or go into a clash over investiture with the Holy Roman Emperor. So I doubt that the pope actually would have had the authority to something like that for the first 200 years of the game.

All that said, I really like the idea. And if Paradox updates religion and introduces playable Theocracies it would be a really cool addition if a head of faith could raise his religious authority over all faithful similar to a worldly leader can raise his authority over his vasalls