If you take over a large city that has all the buildings of the Empire level 4 city, and then you build all of your Level 4 Kingdom buildings. Something just seems wrong.
There is a limit to how may tiles a city can be built on. So if you march into a fully built city, you likely won't be able to build more than a couple extra buildings.
It doesn't give you the option to Raze the city immediately, which i don't like, you should be able to raze it as soon as you march into it.
If you have the proper tech researched, you can select the city, click on the big portrait in the middle of the UI, and choose 'raze' immediately after marching into it. (And there is a bug that allows you to raze a city even without the tech, when you select it and press 'X')