"We don't live in the Byzantine Empire anymore," some people I once associated with would occasionally say derisively about others. At face value, it is clearly true. We do not live in the Byzantine Empire.
Looking at various Greek parishes, the Church building would not always reflect this. Often it is drawn from a definite tradition of Church architecture that is distinctly Byzantine. The same could be said, perhaps, about some canons that (so I'm told) presuppose the Empire is in place, though I know less about that. Most likely we could extend this to other features of modern Orthodox Church life, both within the geographical area formerly belonging to Byzantium, or at least falling in or near its heart, and well beyond, in places such as the United States, Canada, Western Europe, Australia, and Africa.
We should not be so strict with the Greeks on this, though. Byzantium may have fallen, but it is also true that Byzantium has fallen. People remember this. They remember. Cultures have memories and traditions -- it is how they persist as a singular culture through time, and part (only part) of how they enjoy communion with those who have gone before, and how they allow those who have gone before to enrich them even at the level of their secular life. This tradition, this chain, bears one into the present, and in many ways establishes one's identity. To break this chain is akin to mutilating one's own body. The Greeks should not forget -- particularly in Greece and those other ethnoi in traditionally Byzantine areas. They should, of course, remember intelligently, and not select only certain moments for poorly-remembered and drably-rehearsed tawdry festivals of memory to connect climactically with this heritage while kitsch overruns the bulk of their lives in so many other ways, leading to kitschy expressions of kitschified memory.
However, we American converts are only rarely Greek, and so are not in any way Byzantine, and we have our own cultural memory/memories. Often we connect to Orthodoxy because we see that it is closer to certain features of our cultural memory -- which is also not a dead thing. What I have an objection to is the forced assimilation to a foreign memory via structures that displace our own heritage and memory, which memory is often the basis of our appreciating Orthodoxy to begin with, whether it serves as a basis via negativity (i.e., because we see how this heritage fails) or via positivity (because we find that Orthodoxy is the best place to preserve this memory). Unfortunately, Orthodoxy will not be the best place to preserve this memory, this Western heritage, if it insists, either explicitly or simply de facto, on every jot and tittle of the Byzantine patrimony.
A more profound unity is needed than what we have, or else we are simply assimilating to the outposts of a foreign memory.
We must start and end with Jesus, of course.