Civ would probably actually be vastly more educational if it had less historical 'flavor' rather than more: Since basically all the civs, government types, religions, etc. have to be reasonably balanced for gameplay purposes, they all end up being more or less interchangeable and the only connection to the things that they are named after is in the flavor text, city styles, and maybe a unique unit.
The use of historical flavor helps keep things from feeling like you are just playing a spreadsheet(at least for me, Alpha Centauri's unit design mechanics suffered a bit from that: there's no "ah, a swordsman!" it's all "Hmm, is 'plasma steel impact speeder' better than 'synthmetal particle impactor speeder'? let's check the numbers..."); but they are both limited to fairly minor differences, since otherwise civs that mostly lost in real life would be effectively unplayable and they don't respond much to what you do.
If, say, you play as the Romans; hooray, your special unit is the legion. But what if you play as Buddhist Romans dedicated to peaceful persuit of trade and culture? Well, you still get a slightly better iron-age infantry shock unit; because you're the Romans. It would be less flavorful; but more 'realistic' if instead of having historically-based flavor units, your play style influenced the shape of your civilization over time: the aggressive expansionists develop the militaristic culture and units based on specialized tactical doctrines; the culture types get extra soft-power options associated with the fact that even their enemies watch their TV shows, etc.
That would be substantially harder to do right, both in terms of the computer making decisions about your 'style' that lead to 'WTF? The computer thinks I was playing a merchant-prince? I was just funding my giant army!' and in terms of game balance; but it would more accurately capture the fact that what 'civilization' you are isn't just a veneer chosen at the beginning and static throughout history: it's what you do; and what options your choices open or close for you and how you respond to that, and so on.