The coast of Anatolia had been settled by Greek colonists since the 8th century BCE (remember the Persian Wars of antiquity were often fought over the status of those Greek colonies), and the interior was thoroughly Hellenized in the wake of Alexander's conquests so Anatolia was as Greek as Greece during the period of the Roman/Byzantine Empire. Anatolia had a greater importance because it was larger than Greece, more populous and fertile, and it was on the border of the Caliphate so its military value was obviously enormous. Constantinople was impregnable from the land side due to its walls, and enemies in the Balkans typically weren't sophisticated enough to mount seiges, so keeping the Balkans and Greece secure wasn't as important.

Greece itself had been mostly lost to Avar and Slavic invasions of the 7th century. The Byzantines held the major cities (Thessalonica, Athens) and could control the Aegean coast, but the interior was lost to them for a few centuries. Later Emperors actually re-Hellenized Greece with Anatolians!

After most of Anatolia was permanently lost to the Turks, Greece saw a resurgence but that was interrupted by the Fourth Crusade. After that, the Byzantines tenuously held on to a few areas but the peninsula would be a patchwork of Byzantine territories, local warlords, Italian outposts, and Crusader princedoms until the Ottomans came.