A thought just occurred to me, but I wanted to clarify my thinking. Forgive me if this has been discussed ad nauseam before.

I recall that the emperors were dragon born. Was this still the case after the events of Oblivion? I.e. was Titus Mede dragonborn?

Since the Dark Brotherhood assassinate Titus Mede during the life of the LDB (whether or not the LDB was the assassin does not matter) then does our being the Last Dragonborn implies no more emperors? Or perhaps the Empire will limp on, but the emperors will be so far removed from what they have been that they will no longer be deemed worthy of the dragon's blood?

Nope, being dragonborn doesn't give you a claim to the throne, especially now that the amulet of kings is destroyed and the dragon fires no longer need to be lit. Being dragonborn was basically saying you had a mandate to heaven, it's no longer required and an empire can exist without a dragonborn leader.

Really, being a dragonborn means nothing, being an emperor is not decided by the heavens but by who can rule their holdings. The Medes Empire didn't have any dragonborn leaders and the next empire won't either and the empire after that and any empire formed won't have it.

The death of Mede was an arrow to the knee, felt by all good citizens, but the adventures of the Ruby Throne shall not close.

There may not be much of a future for the Empire, at least not for the Fourth Era or a timeline where Landfall occurs. The Elder Council may select another emperor, or it may be possible that a Potentate will once again abolish the need for an emperor in order to "properly defend" Tamriel from the Aldmeri Dominion (which happened once before between the First and Second Eras where a Potentate more or less deemed the role of an emperor as unnecessary). Amaund Motierre never said anything about another emperor taking the place of Titus Mede II after all, and the main reason Motierre wanted him dead is likely because of the White-Gold Concordat that critics say was signed out of cowardice.

Amaund never said anything about anything besides killing the empire and saying a change in policies was needed. It's near impossible to understand anything he has going on.