For starters, the "Romanness" as understood in the 19th century was very, very different from the one in the early Empire. It meant first and foremost being Greek Orthodox, as well as being of "Rum" heritage, as in speaking Greek and following Greek (Orthodox) customs. It was so detached from the idea of being a Roman during the antiquity or even early Byzantium, that it became synonymous for "Greek living in the Ottoman Empire", especially after the Greek War of Independence and the Tanzimat reforms in the Ottoman Empire, when it was no longer such a hindrance to belong to the Rum Millet and the Greeks of the East were considered outsiders in the small liberated Kingdom of Greece.
Greek nationalism was already developed in the 19th century, due to the Greek Enlightenment and it was based much more on ancient Greece than Byzantium. By the beginnings of the Greek War of Independence, Greeks saw themselves as inheritors of both the Great Ancient Forefathers firstly and of the Faithful Christians Who Were Greeks But Called Themselves Romans secondly. If you handwave the first element away, you simply broke the one leg of Greek Nationalism and made Ottomanism a viable project in the Southern Balkans and in Minor Asia. You simply can't have those millions of people considering themselves "Romans/Rhomioi/Rum" in the Byzantine sense as well as getting them to fight for their national independence. Perhaps there would still be some kind of nationalism/localism/elitism among them but it wouldn't give them the tremendous willpower of a national awakening.