The trouble with depicting one of the few Arab leaders who had Mecca as their capital is that they consist of Muhammad and his closest kin, all of which Muslims would rather not see in such depictions. Civ3 got away with including Abu Bakr, but in today's political climate I don't see them risking that again.
By the time of Ali, the 4th Caliph, they had moved the capital to Kufa, so the change seems to have occurred very quickly. The Umayyads moved it to Damascus and the Abbasids to Baghdad, so I think either of those is more likely.
It's really a shame Abu Bakr is a problem with the Shia. He would be such a great alternate leader. The conquering in the name of Islam going on in the 7th century was probably the most successful conquering in the name of a religion in world history and Arabia is not that much a military civ yet (but everything else). So an Abu Bakr that gets rid of Saladin's Building LUA and instead gains an ability that gives every military unit one spread religion charge would be so much welcome. And he had a strong personality and all... But depictions are probably also a problem. Abbasid or Umayyad ruler would also be nice. But an Abbasid would probably focus on science, and Saladin/Arabia in general already does that. So I don't see a huge need for that. Of course, Umayyads or Abbasids could get some commerce or infrastructure bonuses as well... But it's not screaming at me for that.
It's different with other civs, where I think they are too one-dimensional right now looking at their history.
India could do with someone not relying on keeping peace. Asoka would be more into military, Akbar could go many ways.
Frederick Stupor Mundi could focus Germany even more on the Science Victory or diplomacy (may need an expansion for that) and Bismarck is probably the first leader that comes into mind when thinking of a leader getting a bonus to envoys or diplomacy in general.
Abbas could go more into the infrastructure and strong economy thing with Persia, or give them a bonus to religion while getting rid of the (great) surprise war bonus.
Cicero could also shift Rome away from the culture thing and more to a diplomatic victory path in an expansion.
Louis XIV could give France a commercial boost of some sort, depending if new mechanics arise in this field. He could also go culture heavy on other civ or get a flat out tourism bonus on top of the wonder bonus France already has.
Tutmose III could give Egypt a military/expansionist twist. Amenhotep III could give it a religious twist.
China could use a leader that gives them a trade bonus of some sort.
Except for Cicero and Louis, they all would have other capitals than we use now.