One point missing is that Byzantium was, for the most part, in a constant state of decline.
I don't think that America would wish to follow a model that failed. I would rather follow the model of expansion and give up any idea that the borders are fixed. The fixing of the borders is usually the point we look at where the decline of Rome began. The borders I talk of could be real, economic or whatever a nation can do to expand its sphere of influence.
Byzantium did little to expand its sphere of influence and allowed itself to be influenced by others through policies of appeasement in a vain attempt to preserve itself. In the end the Eastern Empire was in name only and through a trackable line of emperors. The Constatine idea of Byzantium had died many centuries before.