Currently being in Istanbul, I've found that the Turks and the government simply don't give a shit about Byzantine history. All funding has been pulled from efforts to keep the land-walls together, the Palace of the Porphyryigenitus is being destroyed to turn it into some short of social space, Studios Monastery is being turned back into a mosque and isn't taken care of AT ALL (I bribed a guard to let me in not too long ago, it's overgrown and like a jungle inside), etc. There simply isn't a large interest in Byzantine history among the Turkish people. I have the pleasure of working with the Byzantine center at Bogazici univeristy here and they constantly try and get more funding and more interest and they're rebuffed. It's really a shame, this city could be a gold mine of archaeology for the Byzantines but nobody does anything about it.

I apologize if this isn't a proper answer (though since it's a question about a field of study rather than a topical question I'm not sure how to make it better), but I'd assume that it's because the Ottoman Empire conquered Byzantium and eventually gave way to the modern state of Turkey after WWI. There's still some bad blood there I suppose.