In my headcanon, Mehmed II is currently wandering through Hell bereft of his eyes, ears, tongue, nose, and hands, as punishment for his snuffing out of such a beautiful culture, and ridding Europe and Asia of its last link to the Ancient World.
EDIT: Only just occurred to me that this may be interpreted as anti-Turkish or Anti-Muslim. I wish to stress that this is not at all what I was thinking, and indeed, I do genuinely like the Ottomans generally (except on EU4 where they are so overpowered as to be insane), but the Classicist within me quails at the loss of the last empire to legitimately bear the mantle of Greece and Rome.
DOUBLE EDIT: I’m sorry, Russia does not count as an inheritor. It was far removed from any of the Ancient civilizations geographically and is more a product of indigenous Slavic heritage than its admittedly heavy Greek borrowings. Neither do the Ottomans since they were really just another Steppe people that had been plaguing Rome and Byzantium for a millennia.