I'ms sorry if it's bad to bring up again a month-dead thread (haven't been on civfanatics for a while), but after reading this thread I can't help but put in my two cents.
The main issue with the civs of Civ is that "civilization" is a very simplistic concept. This was compelled by the limitations of 1990-era technology but is just glaringly awkward now. If we were really to address the problem of eurocentricism in the game (namely, that there are some critical non-European civs that are consistently left out, but we can't include them without removing micro-European civs that are also critical) we would need to create a dynamic civilization system. This is what I think that would entail:
1. Changing the name of the civilization when it changes its system of government, with privilege to examples in history where this has actually happened. So, If, say, Rome were to become Communist it would become the "People's Rupublic of Rome" and get the generic bonuses of communism, but Russia would become the USSR and gain a minor attribute on top of the generic bonus.
2. Using civil wars as a civilizational/governmental attribute. Some civilizations would be more or less prone to civil wars than others, and different civs would be prone to different kinds of wars. China, Persia, and India could be prone to dynastic civil wars, and would each have their set of dynasties which occasionally prop up and try to take over your empire and rename it (or give it a subtitle). A hypothetical "Frankish" civilization could be prone to have different regions more likely to revolt and create new civs such as the French and Germans. All of these possibilities would add minor attributes on top of the civilizational baseline. Another option would be to add civil wars as an attribute of different government types which exert themselves as, say, dynastic or successionist, as I've described here. In all cases, the game would provide mechanisms to control the threat of civil war.
3.Have spontaneously arising cultures within a civilization, under certain conditions. When one civilization conquers another's cities, in time a new culture would emerge in the border territories that combines the two (ie, Greek and Roman would become Byzantine, Chinese and Inca would become... well it would be a thing). As the culture spreads within your civilization you could adopt it as a new name for your civilization, and gain a new attribute, and you might be forced to change your capital to stop it from splitting off. And if the culture spreads into the other civilization, it might eventually enter yours. Similarly, a city that's founded too far away from your core territory, if it stays isolated for long, it might eventually develop its own culture.
The main risk of all this, of course, is that it would add too much complexity to the game. But for the most part these dynamics would be operating under the hood.