I have noticed that when I capture a city in Civ6, sometimes the buildings in a district are damaged even if I didn't pillage them. Which makes me think, perhaps I should pillage everything first if it will need to be repaired regardless.
Is this true, that there's not much downside to pillaging, or am I mistaken? (It's possible they were damaged by the AI in a previous war and just weren't repaired)
More generally, how profitable is pillaging district buildings? Improvements are close to a no-brainer since they're a quick repair by a builder, but district buildings will require some significant production investment to repair.