OK, Christianity is a good argument for the legacy of Rome... although one can argue it isn't strictly a "Roman" product since the original Roman religion was polytheistic. Christianity came out of Judea in the 1st century AD and was persecuted by Romans for centuries until eventually it spread to the elite of society.
My point about Greece is that the modern nation doesn't really have anything in common with the Ancient Greek culture, in any way, and that the hero-worship of that culture in modern Greece is artificial, fake, phoney, a fraud, and largely a product of 19th century nationalism.
Greece's actual culture owes far more to the Byzantine period, as I've said earlier. But that is downplayed, for "reasons" that have a lot to do with modern history, and not much with ancient times.