First; tell that to the HRE, Italy, the Balkans and later Ottoman Vassal States, Japan, India, the East African Coast, West Africa, Arabia, the Caucasus', Indochina, Indonesia, the Barbary Coast, Mesoamerica and North America. It wasn't until the mid-1600's that nation-states began truly emerging, and even then there have been plenty instances in history before of 'small states not faring well in this era' such as against ancient Assyria, Persia, Macedon, Rome, etc. Second, Byzantium's Army wasn't private during this period, primarily because they didn't have much of an army to begin with. Third; how would Byzantium surviving go against every trend of the period? If they survived by some harebrained miracle (or a successful Varna), then that would imply they would have had to adapt to the period to do so.