Wouldn't most people go along with it? At the end it just needs to be a name people can identify with. So for example renaming Germany HRE is something people can connect to, renaming it Frankish Empire wouldn't work.
Let's remind ourselves that the name Byzantine Empire is historiographic and not actually the one BYZ used. They called themselves Imperium Romanun, i.e. Roman Empire. Who in their right mind in the 30s/40s would take that seriously? And I don't even mean abroad but even domestically: who in Greece would have the gall to claim the Roman Empire reborn in the southern Balkans and a bit of Anatolian coastline? A Greek state claiming themselves as the Byzantine Empire would make little sense to anyone, at that point, just plain call it the Hellenic Empire.
You can't have one without the other. The Greek kings were considered legitimate successors to the Byzantine Palaiologos Emperors (Constantine I also went by Constantine XII), restoration of the Byzantine Empire was always a possibility (even if not a stated goal), and it's no more ridiculous than restoring the HRE (and I would argue less).
I've never heard about the Kings of Greece claiming to be successors of BYZ, I'm going to need a citation on that.
Furthermore, the Megali idea was about Greek nationalism: Greek land for Greek people. BYZ is about claiming all the ERE lands to a lesser extent and the whole SPQR lands to a greater extent, no matter the nationality, culture or religion of the people living in the 20th century there. Seeing that Greece controls less than 10% of the ERE lands and less than 5% of the SPQR lands in 1936, and Germany controls maybe 75% of HRE lands (sans Kingdom of Italy) in 1936, then I would argue an attempt to reform the latter makes a bit more sense.