Looking back into the past from the distance of two thousand years warps your sense of time. Alexander's empire crumbled quickly, but many other great ancient and medieval empires lasted for centuries or millennia. To use the Maurya Empire in India as an example, that's a relatively short-lived polity compared to Rome or China, but it's still literally longer than you can imagine, longer than any human being has ever lived. South Africa has only been around for twenty years, and may yet collapse into violence (as an unfortunate number of postcolonial nations already have).
You say there are a large number of big, stable modern countries. I say you can count them on one hand. Compare modern nations to the Maurya Empirehow many have lasted 137 years? Go back to 1876, find major nations that haven't experienced violent regime change. There's the United States, there's the United Kingdom (although it has lost almost its entire territory). Denmark, the Netherlands, and Sweden may not be major nations (and two of them were invaded by Germany in the interim), but they're major enough for Civ 5, so we'll count them. It's a bit of a stretch, since they had a democratic constitution forced on them by the US, but we could include Japan, since the Emperor has remained the nominal head of state this whole time. Throw in Switzerland, which is definitely not a major nation but certainly a stable one.
So: seven nations if we're being very generous; one if we're being strict.
Now think about ancient Egypt.
Okay
a) People are going off on a tangent here ... my response was that archeology was part of the mechanics that start to reflect a little more realism into the late game in that larger stable countries will in theory get more archeology sites whilst smaller focused empires got the better of the mechanic earlier with things like great works. I actually think design wise it's a pretty elegant way of reflecting one of the advantages of size where the old mechanics punished that a tad to much.
b) You are going off on a tangent somewhat in that things like United Kingdom and the Netherlands are small ... they aren't large ... they may have had empires but Empires are different to large countries. Why you are bringing in Denmark is a mystery to me.
My point was and still is that in modern times it's easier to have a truly huge country and not have it fall apart. Even when regime changes occur. look at Chinese history and there is a history of splintering and conquest leading to reunification followed by another split.
Australia, Argentina, Brazil, USA, Canada, Mexico, South America, China, India, Russia and Indonesia are all extremely large in terms of size in historic terms and even when some of them have experienced tremendous changes in government over the last 150 years they have'nt splintered into numerous sub groups. Russia went Communist and back again and eve after communism fell most of it's areas stayed as part of Russia rather than risk going off on their own. China went Communist, USA suffered through a short brutal civil war, India in unification and partition, Canada and Australia were released from the Empire and given independence, South Africa threw off the shackles of Apartheid etc etc. Societies of that size in the pre Industrial era rarely survived such upheaval. The Industrial era brought many things and one of them was cohesive large nations that dont splinter as easily. The more modern and the better your technology you are the more stable you tend to become despite size.
I see Archaeology as being in a small way one of the compensations for larger civs within the game in that you may have access to more sites within your territory. It's a small offset to the negatives the game throws at you for being wide but the CN Tower and that do go some way to giving larger civs some late game cultural bonuses reflecting reality.