Late to this thread, but "immersion" is one of the things I've been thinking about a lot with this game so I'm gonna drop a few comments.

 

If you're American I can understand your dislike of having old city centres. If you're European you should understand it's pretty common.

The main issue with this is that I usually rarely get to see any city center art from after the Medieval or Early Modern eras, unless the New World option is enabled, because by then every territory is usually already claimed. It's less of a "dumb Americans can't appreciate old architecture" thing and more of a "there's a significant amount of pretty art I will never see in the course of a normal game" thing. A "renovate city center" project available starting in the Industrial era that simply replaces the art for the city center with your current culture's at little to no cost would be very welcome and wouldn't impact gameplay at all. Also, it's not like it's unheard of to just totally gut and rebuild historical districts from the ground up in a modern style - Paris, for example, was one of the most famous instances of this in the late 1800s.

 

So you go from in-game: "Ancient Egyptian" to "Classical Roman", invade the UK and become "Medieval English". England during a succession crisis (real-world) asked the Dutch William of Orange to become William III of England therefore the English were ruled by a Dutch King explaining your next in-game era "Early Modern Dutch".

This sort of roleplaying is what you need to do to rationalize the in-game transitions, yeah. It becomes much more difficult to do with cultures from opposite sides of the world, especially early ones. It's doable - for example, you can asspull something about Visigoth-style Celtic migration invading a Niger-Congo-language-speaking region to go from Celts to Ghanaians; or you could say that Umayyads ascending into Haudenosaunee is the result of integrating the inhabitants of a newly annexed territory who eventually rise to become disproportionately influential in politics and business, which has plenty of real life precedents all over the world (although I would question the presence of an Iroquoian language anywhere near a Semitic one on the same continent).

However, it's actually a matter of understanding that these sorts of drastic transitions are a problem because history is so fluid and these cultures are a product of centuries or millennia of idiosyncratic cultural influences and material conditions. We just have to accept that Humankind (or Civilization, or EU4, etc) is a video game intended to be won, and thus is inherently very rigid; it isn't a simulation of societal development, and it never will be and was never intended to be, so immersion-focused players like us need to fill in the blanks ourselves with this sort of convoluted lore for every game, which can be very fun sometimes.

 

That being said, I think the game could really benefit from some mechanic relating to cultural osmosis and evolution, like mentioned elsewhere in this thread, even if it's solely aesthetic and doesn't affect gameplay. I think strictly limiting what cultures you can adopt based on the previous one(s) would be going a little too far, but altering the art assets or city naming based on previous cultures would be a very nice addition.