Remembering my lore to the best I can, it says that only a Dragonborn can light the dragonfires and become Emperor/Empress, the Septim bloodline descends from Tiber Septim, a Dragonborn even he was of Nordic decent, but upon service of the Colovian king he become very, 'Cyrodiilic.' And the Septim line has been of prime Imperial stock.
I know that lighting the dragonfires is no longer a precaution, and the Amulet of Kings was destroyed. But does it still not stand as a symbol of the Empires devotion to Akatosh, and the union of blood between Akatosh and Alessia. Playing the game as an Imperial, if the covenant between Akatosh and Alessia still stand and as you are a Dragonborn and thus carry Dragon Blood in your veins does this not make you a technicality to become the ruler of the Cyrodiilic Empire?