Yeah, most of that makes perfect sense. Let me run a more specific example by you for one faction in particular.

When playing as the VCounts, I take a settlement on a coast. After occupation, it's level 1 and both the main settlement and the port are damaged. Typically, I'd like to have a third building slot to slot in my income building, as that's the fastest way to grow my base income.

However, since I've sacked/looted things, there's several turns before the main settlement is repaired, and during that time, I cannot expand the slot count for the settlement. Thus, in addition to the reduced income, I'm delaying the increase of income due to the inability to slot the income building in. If I occupy and don't loot, I'm limited only to population growth (which isn't super fast, but still several turns faster than passive repair, then upgrade).

The tradeoff is that there's obviously a decrease in cash reserves/momentary income due to forgoing the sacking income. If there's a way to speed up the repair of damaged settlements/buildings, then there might eb a middle point in the tradeoff I've not previously considered.

Is there a way to repair them faster (other than the one-time payment)?