Because Islam in faction specific religion. Think about the other religions, they are either faction specific (Hinduism/Buddhism). Islam founded a civilization, it combined a people, hence the reason why Rhye had the religion spawn in Mekke.
BUT... how about we just have Islam spawn in Mecca in 632, thats also an option which I would be up for. Fair enough its three turns, but then how about just have Islam spread later, because as mentioned earlier Mecca and these other cities were already founded.
I like your idea, but I still think a Moorish civilization should take its place, rather than the Arabs getting far flung territory. Also I'm afraid it would unbalance the fabric of the game
A Carthage respawn would work well as the Moors I guess...