While it's true that Greece was not an Imperial military power after the rise of Rome and Persia, much of their culture and history was preserved (Ironically their Turkish enemies saved much ancient knowledge.) and lived on to be reborn as the Eastern Orthodox Church/Empire.
Roman history, law, ethics, logic and science, much like the earlier Greek is taught to this day. And the Roman Catholic Church/Empire has been wildly successful by any stretch of the imagination.
Historic Empires have that kind of staying power. Even short-lived Empires, like 20th century Imperial Germany and Japan, do much to shape the future. Fairy tale Kingdoms, on the other hand, are reduced to a couple lines in collections of myth.
So. First one must define what one means by the "fall" of Greece and Rome. Then you must demonstrate some correlation between homosexuality and that alleged fall. Finally, one must provide a single shred of evidence: a wall, a fort, a coin, a tablet, a coin. Any physical evidence for the existence of your Biblical examples would really help support your suppositions.
Oh, yeah, I almost forgot. If you find evidence for the existence of your alleged examples? You still need to demonstrate that they were destroyed by the wrath of God when he grew upset with their sinful ways.
