The only reason I can think of was the fact that Constantinople was not going to fall into Roman/Greek hands anytime soon and the Roman/Byzantine empire was pretty much tied to Constantinople. But still, given how the Greeks yearned a restoration of the empire, surely they would have settled for a small part of Greece for the time being, with the dream of restoration always lurking.
I would suggest, until you receive a full answer that you research the Philhellene movement which gripped the west in the early nineteenth century. These intellectuals and poets, of which Lord Byron was the most prominent romanticised Greece's Classical past, adventuring in Greek lands and temples.
So it came about that when the war of independence was called in 1821 it was originally on highly ethnic and religious grounds. Greeks massacred Turks in Hellas, and the ecumenical patriarch of Constantinople was executed for failing to dissuade the rebels. He was hanged and thrown into the sea and collected only by a passing Russian ship. So it could have easily been a renewed Holy War but for one thing.
The actual war was not successful for Greece. They suffered grievous losses and we're eventually confined to the Peloponnese. The cultural resonance of Greece was not Byzantium, it was the classics that every boy read in school. It took the death of Byron while besieging Messalongi in 1822 to cause massive popular support to call for foreign intervention. It didn't come but as the years dragged on in 1827 an allied force of the British, French and Russian navy at Navarino decisively crushed the Ottoman navy almost to a single ship. The war was a mess but only Russia wanted a Christian. When the monarchy was introduced after all, it was granted to a German Prince.
I'm a Byzantinist, I've only written two papers on this in university as part of a broaden-your-knowledge module so I hope a true enlightenment nineteenth century specialist picks this up.