First and foremost Greek culture was much more deeply rooted than the Ottoman one since it predates even Islam by more than a millennium. There were those who adopted the prevailing faith and culture, but they were always a minority. Perhaps given enough time ‘Greekness’ would have been drowned out but it would have taken much longer than five centuries. For example, Constantinople- the capital of the Ottoman Empire- had a significant Greek populace and character until the population exchange of the 1920’s. The same is true for many coastal areas in modern Turkey. They remained Greek Christian enclaves until the exchanges of the twentieth century.
A second reason is that much of the Ottoman energy and vitality had been expended by the time the Greek heartland was taken. For a century it appeared as if the Ottomans couldn’t be stopped, but when Suleiman the Magnificent besieged Vienna in 1532, his failure to take it marked the beginning of a 400 year decline. The Ottoman Empire became a bloated, weak figure- christened the ‘sick man of Europe’ by the Russian Tsar. (You know you have problems when you get a derisive nickname from Europe’s most corrupt monarch whose own empire is about to collapse) At the same time there was a growing European appreciation of all things Greek which fueled a new wave of patriotism. Since the ‘re-discovery’ of antiquity during the Renaissance there was a steady stream of pan-Hellenic feeling – best exemplified by Lord Byron who wrote and fought for the Greeks during the war for Independence. If there was any question of Islamic or Ottoman culture supplanting the Hellenic one it had vanished by this point.