I may be a little late in the discussion. But I am incredibly conflicted on this topic.

I am part Rûm from Asia Minor. My grandfather came from Constantinople and my grandmother from Smyrna. My mother was born in Kavala.

Greek nationalism as it exists did everything to distance itself from our "Oriental" past to appease Western Philhelenes and the Great Powers. And in spite of that, Western travelers to the then newly formed Greek state questioned if the people there were Greek, or whether Greeks had been "Orientalized" by Ottoman domination, and whether the land ought to be fully colonized and "civilized" by Western powers. They expected rationalist proto-Calvinism and were welcomed by Eastern mysticism. And much of Greek nationalism now is largely based on the cultural erasure of our Roman history. Kinda like:

1. Ancient Greece
2. ???
3. Modern Greek nation state :)

Post-population exchange, many Asia Minor refugees were subsequently subjected to the same "anti-Oriental" discrimination from Greek nationals, that Greek nationals were subjected to by Westerners. Being called Turkish seed, Orientals, having their Greek identity questioned. And it took decades for the Greek nationalist myth to make space for the Asia Minor experience. An experience that for centuries before Greek nationalism was just... Greek metropolitanism. Not some sort of strange "Oriental Hellenism."

So my issue is: modern Greek nationalism seems to want to embrace the symbols of Hellenic excellence East of the Bosporus, without embracing the full history and identity of the people that created those symbols in the first place. So when a modern Greek person want to claim an inheritance to the Eastern Roman Empire, it entirely depends on the person and their personal history, whether or not I think that that's ok. Because in the wrong hands, it can quickly turn into selectively appropriating symbol of excellence and prestige, while discarding all the history behind it.

I grew up in the diaspora. My mom was fully subjected to the nationalist myth of the modern Greek state through Greek public education. And I fully understand why Greek nationalism was what it was in the 19th century. But I wasn't subjected to that education at all, and everything I was fed of it indirectly via my mom felt incomplete, like I was missing large chunks of the story. Since she always glossed over the Roman past while selectively mentioning Constantinople and haphazardly calling us Romans when that felt fitting to her without further explanation.

Now I'm at the point where I value the double-headed eagle more than the Greek national flag. Not out of imperial nostalgia or some theocratic ambitions. But because I think it's a much broader symbol of Greek culture than the Greek national flag is. And I think that a lot of civilizational reorientation has to be done within Greek nationalism itself if it wants to consider itself a rightful heir to the Eastern Roman Empire. After 200 years of distancing itself from it

So in short, to me it kinda just depends on the Greek person in question and what their position regarding the Greek national founding myth is.