I'm not an expert but this is something I've also pondered and these are my thoughts on the subject.
Its my understanding, primarily from listening to History of Rome and History of Byzantium podcasts, including the interview in regards to the book "Byzantine Republic", and pondering on it that the difference between the feudal monarchies and Byzantium was that the former were de facto and de jury monarchies. While both Roman empires never became a de jury monarchy, to my knowledge. The difference thus is that there was an open celebration and of the monarchy into an office that wasn't just like any other and that it was tied to inheritance in the feudal world while in the Roman empires it was to my knowledge not so that the office of "emperor" was publically celebrated as an unobtainable strictly inherited office. Elevated yes, sanctioned by God, yes, but not strictly inherited and unobtainable in any other way.
Thus while the French nobles would have been taught from birth that no one save the close relatives of the king can become kings, the Byzantine nobles would have been taught that the office of emperor was just another office, one that was subject to nepotism, yes, but still not an unobtainable thing forever beyond their reach by the will of God. As such I think that it was the republican inheritance of Rome, and that it was never really fully shed, that made people less struck by awe even by a high office holder. Not to mention that while most French kings and dynasties, for example, to my knowledge came from the top of the nobility, many colorful characters not from the top of the elite did take the position of emperor in Byzantium.