That’s not even arguably true.
You could debate whether or not the Roman Empire fell in 1453, if we’re pretending that the Byzantine’s represented a cohesive enough continuation to the traditional empire as we understand it. For the record, I don’t subscribe to that idea. But it’s a debatable topic.
But Rome, the City, had nothing to do with the empire after 476, and arguably even earlier since the capital of the west had moved on to Mediolanum a long time before that.
Or you could argue that Rome never fell for good because it is still/again a capital city and was only not a capital city from (around) 476 to 756 when Pippin the Short gave jurisdiction over Rome to the pope and created the papal states.
Rome means the empire, the kingdom, and the city.
WHAT ABOUT THE REPUBLIC
Sorry. I’ll report to the nearest legate for my 30 lashes.
Not good enough. I’m afraid this requires a decimation. Choose ten of your co-workers.
Byziboos vs. Latinboos, FIGHT
The Roman Empire fell in 395, the Western Roman Empire fell in 476, the Eastern Roman Empire in 1453 and Rome as the capital/seat of government of the/a Roman Empire “fell” at the turn of the fifth century when the seat of government was moved to Milan (or, Rome as a city fell multiple times to invaders).
Alternatively after 1453 the Russian Tsars claimes to inherit the legacy as the ‘Third’ Rome. That lasted until the Bolsheviks.
I mean, that’s about as much Rome as the Holy Roman Empire…
Which only lasted until Napolean. But there were a few decades where they had at least some holdings in and around Italy.