It's hard to say the Roman Empire "lasted" after the city of Rome was sacked.
Not at all. You may define Rome by the city itself, but "Rome" itself did not once Constantine had moved the capital and senate to Constantinople.
Constantinople wasn't even originally part of the Roman Empire, it was conquered later when they grew really large.
Hoo boy, is that ever off. Constantinople didn't exist before Constantine created it, and he did so with the explicit intent of moving the capital of Rome there, to the real hub of the 4th century empire.
AFAIC, you can't have something called "the Roman Empire" if it doesn't include the Italian peninsula and most especially the city of Rome.
AFAIC? OK, then you're being blatantly arbitrary. Did you intend this misconceived analogy to strengthen your argument? It does the reverse. Federalism has its merits, but I suspect from the above that your understanding of the real issues is rather thin.