While there's some truth to this, I think separation of church and state is stronger in the western tradition simply because the western empire had no political

While there's some truth to this, I think separation of church and state is stronger in the western tradition simply because the western empire had no political successor. Had, for example, the Carolingian empire persisted as the new Rome I believe separation of church and state would have been weaker in the west. As another example, the eastern empire did become more of a theocracy as mentioned in the first passage. I think separation of church and state is simply more likely among a constellation of petty kingdoms than it is within an empire.