It was explained by devs, and I basically repeated in my post
here: you need to break the concept of Civ cities as "cities" and treat them more as provinces: There is an administrative center (the "city"), and then there is different supporting quarters/hamlets/towns/sites (the "districts"), which depend on the city center for government / administration / community. Military it works, because if you conquer the citadel/city center the different districts should then gets its administrative support from you and not from the former owner (altough I won't object a more dinamic management of districts, with the option to re-assign them to different cities), and probalby the district inhabitants have fleed nevertheless to the city center for protection...
As
@Zaarin said, it is not matter of making a district a city on its own, but a matter to make it easy to underestand visually a city represents a full province, with several urban centers, with the one named the city the being "core" one, to which all others are satellites.