Agree that many, especially in the later and maybe even middle depending on dates would equate being Roman to being Christian.Without a doubt it's more complicated than that, but I think my main point was that for a significant fraction (depending on which arbitrary dates one wants to pick as "beginning" and "end", possibly even a majority) of the empire's life, the concepts of "Being Roman" and "Being Christian" were very much intertwined - like I'm pretty sure if one could talk to someone living in Constantinople in about 450 CE or so, they would say one couldn't be Roman without being Christian, if they would even recognize the two concepts as distinct from one another. The whole idea of a separation between nationality and religion is a pretty modern concept.
I'd also argue that Rome itself ceased to be the capital of the Empire round about the crisis of the 3rd century - particularly by the era of the Dominate the "capital" was wherever the Emperor happened to be (which definitely gets messy during the Tetrarchy because there's four of them).
The fall of the West probably was inevitable, but the lesson I draw from it is that Rome as an institution failed to do what it had done many times before - successfully integrate a new population (in the final case, the germanic/frankish peoples) and get them to buy into the concept of the empire. They'd done this a LOT over their history - one could measure the life of the empire as which region provides the leadership for and maybe "driving force" of the state; starts in Rome itself, then moves to the surrounding Italian cities, then Greece, Hispania, North Africa, Dacia/the Balkans, etc. I suspect there's a thesis for a book in here somewhere.
That's actually the parallel I'd draw with the US - we've also successfully integrated disparate populations and gotten "buy-in" on the values and ideas we (claim to) espouse over our history and (in my opinion) gained strength by doing so. Are we reaching a stage in our development where we're not able to do that anymore? Maybe. But I don't want to get this thread banished to the Cave, so I'll stop there.
And yes, you are correct that the capital moved and in general was where-ever the Emperor was. Or at a later date in Italy it even stopped being Rome and moved to Ravenna, if memory serves, partially or mostly because that city was more defensible.
But my point was more that Rome as the cultural heart , so to speak, not a perfect analogy I understand, but that started changing once the capitals started moving with the emperors, once Constantinople was founded and growing, Rome was challenged within the empire as 1st city in a way that it hadn't really been before..
I think to some degree you are correct that Rome stopped integrating and that lead to its down fall. I think also, there was some disconnect from its peoples. For example you have the two very different views of society from the West and the East, the Latin vs. the Greek speakers. Sure, there were commonalities but in some ways, I think Rome's fall was that it not only failed to continue to integrate, I'm not sure towards the end if it did a great job of actually creating a common thread between the different groups of people. I think initially there was a very strong connection between being Roman and what that meant. I think the problem for any country,
or empire, for that matter, once it gets to be a certain size and of a certain level of diversity, is that establishing that common thread can be difficult. Look at the US today. How different are the culture norms, beliefs and customs of people if you go from California to Texas to New York city then to Alabama than to Alaska? I think that also played a role and was a double edged sword. Diversity and expansion helped Rome became what it was, but I think eventually it also was one of the pieces that perhaps lead to its downfall.
I think it was a bit of a catch 22 just like it can be today. The benefits FAR outweigh the risks to me but even though everyone in the US lives in the same country, I'd argue we're less united than too many earlier times in our history, which, granted, from a historical context, we are still very very much a baby.
I think to some degree the size , wealth and diversity of Rome, while as a strength also laid the foundation for its collapse. Because some of its unifying principles from earlier in the Republic or early days of the empire I'm not sure if they were as strong as they once were.