On these questions, a lot is up to interpretation. Claiming certainty is a fool's errand.
Re your analogy, it would be more like if the US moved it's capital to LA because California is richer, better positioned, etc. lasted for a few hundred years in that form, and then it lost everything east of Kansas City to unwashed masses of warring right wingers, who took over and turned that part of the country into more independent "states" led by war lords.
It's true the empire in Constantinople thought of themselves as Romans. But they gave up Latin at some point and only spoke Greek. And dating the fall of that empire to 1453 can be easily challenged. In the 1200s the Crusaders conquered Constantinople, sacked it, and remained for 50 or so years. That sounds like an ending to me.
The Fall Before The Fall: The Latin Empire of Conquered Byzantium – Part 1 - Medieval Ware
The end of the Fourth Crusade was not marked by the retaking of Jerusalem or even the defeat of the Crusader armies – it ended with the Sack of Constantinople in 1204: the systematic looting and destruction of the collected wealth of the Ancient World by a few thousand greedy Crusaders. When the...
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