Honestly, it should depend on the empire type.
In most empires, "factions" should play a greater role, both at a planetary scale, and at an imperial scale. Individual characters should just be extensions of factions, more like the face of individual factions, than characters which can change everything on their own.
For example, the current leader of a cartel on one of your planet could have an impact on how hard they are to handle, or how willing they are to negociate with that planet's authorities.
Or the current leader of a dynasty within your feudal empire owning an entire sector could have a say in the support they bring to their emperor. And he should probably have a bigger impact than a very temporary governer appointed to a random world - after all, you're delegating power to him.
But in the end, the real "players" are the cartel itself, or the dynasty itself. Characters are merely temporary faces for organizations that should play a greater role in game.