Interesting overall point, but several comparisons that I either disagree with, or is plain historically incorrect.

No, we are not the Byzantines. The US right now is more akin to 2nd Century Roman empire at its peak of Hegemony and military might.

That would make China more akin to the Persians of that time, IE our lesser rivals, but also huge trading partners with us, and we ultimately both benefit from each others success.