I wonder why this thread was top of page in the news, no matter.

As a general rule I demolish it and build the magistrate line to allow better repression for one thing. The proviso of course is that you may want to trade one of these usually economically poor provinces immediately for something else like another province in a more strategic place, or a trade agreement, protectorate or techs. Then I wouldn't waste the money to demolish usually is was damaged anyway when you took the place.

On general building demolition I suspect this is a neglected part of many peoples game, most importantly is demolishing other religion buildings and building your own, also using wealthy towns for economic purposes rather than a school or religious thing, leaving poor one to do those jobs.