If only the British would have allowed it!
At that time Constantinople was still 1/3 to 1/2 Christian (Greek and Armenian), and Eastern Thrace and the City could have very easily been given to the Greeks as war booty without many problems.
The paucity of reward and support for the Greeks after WWI is the direct cause of the present problems.
The British never could understand what to fight for besides their own wallet.
Glad you brought this up. Imagine a Turkey with the western end belonging to Greece and the eastern end belonging to Kurdistan.