> Byzantium was never actually Greek, many emperors didn't even speak the language.
Huh? I'll admit I'm not that well-read about Byzantine history, but I had always been under the impression that from the reign of Heraclius (mid-7th-century) onwards[1] the court language was always or virtually always Greek.
[1] Which is also as good a dividing line as any between the "Roman" and "Byzantine" periods.