The problem with this approach is how much it would squish entirely different nations/ethnicities into one blob.
If it were done poorly and without knowledge of real unique qualities, yes, but I'm not suggesting that it be done poorly.
How would you do a Sumerian civ, for instance? Or the Aztecs? What would you call them? I guess Mexico and Iraq?
No, I would call them Sumer and Aztecs (well, correctly, the 'Triple Alliance') just as the game does now. And, just as the game does now, any uniques for them from after the period in which they existed would have to be 'generic' based on their terrain/climate preferences - just as the game does now.
This whole issue just stems from lack of a clear definition of a civilization by firaxis. A lot are specific empires, some are regions, or countries.
We generally expect the regional civs to include the whole swathe of history in that region, while the empires stick exclusively to their time period. The countries are the toughest as we expect them to cover a lot of time, but only the periods of history that most remind us of their culture.
The problem actually, is lack of a clear definition of a 'civilization' by everybody: Firaxis and the Player Community both. Precisely, a Civilization is a group that builds and lives in Cities. That means, even by the widest possible definition of 'city', many 'civilizations' in the Civ franchise were never civilizations: Huns, Iroquois, Commanches, 'Polynesia', etc.
Most people, and Firaxis from their actions, widen the definition to include any recognizable cultural/political group. That leaves everybody with the problem that this definition includes numerous 'groups' that were either extremely short-lived in game terms (Sumer, USA, Carthage, Huns again) or over time included numerous other cultural/political/linquistic/ethnic influences, to the point of changing their nature completely. In strictly historical terms, in 4000 BCE there were no recognizable Greeks, Romans, Germans, Celts, Huns, Scythians, Chinese, or any other of the 'Civs' included in the game. They all developed their recognizable characteristics within the time frame of the game.
So, from the beginning, Civilization the game was a fantasy game, and so it remains.
And, I think, so it will have to remain.
Think about it. To do otherwise, you'd have to start with a wandering tribe with pretty generic Neolithic Attributes in 4000 BCE. Yes, some 'tribes' have pottery, primitive boating, Animal Domestication, or Agriculture, but none of them are building anything 'unique' yet, or showing more than the Photo- versions of their languages or religions.
Then, to progress to 'recognizable' Civilizations, you'd have to model the influences, and (I've thought about this a lot) that is monstrously difficult.
Just, for example, the Greeks: start as nomads, wander into an area with fertile land next to the sea divided into 'compartments' by mountains, already inhabited by an agricultural people. The 'Proto-Greeks' conquer them, absorbing some cultural/religious/technological/linquistic elements from them. Then they interact with other civilizations like the Hittites, Minoan Cretans, and (early) Phoenicians. Then the Mycenean Bronze Age civilization collapses, and out of the Greek Dark Age comes a set of city states with Aristocratic/Oligarchic governments relying on citizen spearmen who insist on a say in government and so develop various forms of inclusive to semi-inclusive Democracy with Hoplites - and semi-secular Philosophy, which comes from of a way of looking at the world and examining it almost unique in the entire world.
Bluntly, not once in a 100 games will you get a recognizable Greek Civilization by the Classical Era, because the various cultural, technological, climactic and geographical influences make a total that is very nearly statistically impossible to reproduce.
And that is very nearly true of ALL recognizable civilizations in history.
So, we go with fantasy, and start the civs with recognizable but anachronistic Unique Attributes and assume they will still be recognizably unique even thousands of years after that particular civilization historically disappeared.
What I would like to see is not 'historically accurate' civs - an impossibility even if we knew exactly what that meant in every case, which we don't - but more dynamic Civilizations that may or may not develop the same way every time based on the in-game conditions.
What If? is always an intriguing question, but right now, I don't think the Civ games provide a good answer.
What If - Greeks developed a wide empire, and maintained it? How would that change their political/government/cultural uniques.
What If - outside monotheistic religions did not influence Greek religion? What kind of religion would they end up with by fuzing the old Polytheocratic Agglutinative 'Hellenic' religion with Greek Philosophy?
What If - The Greeks did not settle in a climate/terrain like Greece, but on the Eurasian plains/steppes where they came from, or in a volcanic semi-tropical area like the Aztecs? How would that change the Unique Attributes they develop? Right now, the game assumes that it would have no effect on them at all, which is ridiculous and forces the gamer to deal with the map without the adaptability of the historical peoples.