It would be strange to have a race-less, name-less, gender-less, class-less, everything-less Emperor in lore.
And the Dragonborn has no right to the throne, being a Dragonborn doesn't give him any right by itself. The emperors before and after the Septim weren't Dragonborns. Conquering the throne is what gives you the right to the throne, people didn't give the throne to Talos, he conquered it.
(Not to say that Martin Septim probably isn't even directly related to Talos)
I don't think you are correct.
Alessia's (1st Empire), Reman Cyrodiil's (2nd Empire), and Tiber Septim's (3rd Empire) heirs were all Dragonborn. This is not to say that Dovahkiin is heir to the throne just for being Dragonborn, but I am simply stating the past emperors were. Martin is a direct descendant of Tiber Septim, as his father is Uriel Septim VII and Uriel is a descendant of Tiber Septim, hence his crowning as emperor.
I wouldn't write off the idea of becoming emperor though. I certainly wouldn't mind a canon-Nord emperor, although others would certainly get angry at that decision.