then with this option any new building will have the aesthetic from the current ones and not previous ones, right?

Yeah, I also find it jarring when your people tear down old stone buildings to build new ones made of wood or straw.  I made a similar proposal a few months ago that includes what you're asking for:  The idea would be that when you change cultures, your cities keep their current appearance and slowly evolve over time, with buildings from older cultures slowly being replaced by buildings from your new culture.  If it were slow enough, then you might even see buildings from three or more eras at once.  

And as Daarkarrow has asked/implied, the idea would be that your new districts would match the aesthetic of your current culture, yup!

Daarkarrow wrote:

then with this option any new building will have the aesthetic from the current ones and not previous ones, right?

What I had in mind was more something like that: 

- ancient era: Zhou

- classical era: Celts. all your buildings evolve to match the classical era style, but not the European, the Asian. New buildings would still have the classical Asian style.

- medieval era: Mississippians. all your buildings evolve again to match the medieval Asian style not the Mississippians. new buildings have the medieval Asian style

- etc. 

In this approach only the EQ and administrative centres for new cities would get the Celts, Mississippians, etc. style. 

Of course this could also be a little jarring but not as much as a total change. 

with that said, If I understand what you mean correctly, it would mean that our cities would have a mix of Asian, European, American buildings?? That sounds like it could be either super interesting or really weird :) 

but would that mean that, at the modern era, only the outskirts districts would have the modern look??

Come to think of it, if people play the game as much as a city builder as a 4x game (which is why I do most of the time) the really best option would be to be able to click on any districts and select a style based on the cultures you have chosen. that would be super granular and, that way, we could really design our cities with various districts like an Asian medieval district in the middle of a European industrial city or something like that.

I would love a feature like this as well: nothing makes me sadder than moving on from the Franks and seeing all those wonderful cottages and gothic basilicas disappear. Of course, there's no need to go crazy here: while a highly granular system where you could select every district's style would be cool, it seems too ambitious to implement: this is still a 4X game, and one wouldn't want to bog it down for cosmetic reasons. What about a one-turn project (in a similar vein to the one that updates the city center) like "lock district style to current era," that could be used on any of the regular FIDSI districts or a Commons Quarter? (Probably not Garrisons, though, as, say, a stone castle would be non-functional as a garrison in later eras.) Then, the player could save a few favorite "historic districts" before moving on in each era, but it wouldn't require making a new UI for the feature.