"I want to become Caliph instead of the Caliph"

It seems that Iznogoud (with his famous catchphrase "I want to become Caliph instead of the Caliph") is getting pretty tough competition these days! First it was ISIL/IS/ISIS/Daesh, then Boko Haram and finally (or rather more recently) a refutation from 126 scholars and clerics.
Now I know why my middle-eastern friends would get so worked up when I would mention the Cordoba Caliphate! Well, I am not so sure myself that Abd-ar-Rahman was really the only Umayyad left after the Abbasid killing spree, but that is for others to debate. It seems that, like in Highlander, "there can only be one"!! A Caliphate represents a sovereign state of the Ummah (the entire Muslim community), and given that unity of the faithful is paramount (this could also be a reason my friends were dismissing the Cordoba Caliphate, it was competing directly with the Fatimid Caliphate in Cairo and indirectly with the Abbasid Caliphate in Baghdad) a single leader and entity are required; a bit like the Pope and anti-Pope(s) of Catholic tradition.
One of the key arguments, based on Islamic jurisprudence (Sunni interpretation), against ISIL Caliphate is that it requires general consensus... and so far pretty much of the consensus is against. Maybe good old Al-Baghdadi would have been better off claiming a Shia Caliphate/Imamate where the majority is not necessary as it is divinely chosen (if the genealogy not checked too closely). But I think that bridge is well burnt by now.
Nevertheless, this Caliphate claims are more a political statement with religious connotations rather than the reverse.