Don't most Chinese dynasties get seen as successors, despite having destroyed the preceding state?
That's only because The Mandate of Heaven as far as dynasties went is that as long as a dynasty has divine favor it can rule, but if they lose that favor. ie tyranny,natural disasters,discontent then who ever overthrows that dynasty would be legitimate. Provided nothing like the 3 Kingdoms came about.
I don't think there is a similar president with the Roman Empire,even as dynasties changed and emperors came and went. So how would we determine what is a continuation of the Roman Empire? I doubt anyone would think The Holy Roman, Latin, and Russian Empires would be a continuation of it as well the Ottomans.