Looting in a region only lowers sympathy to your realm in that region, not the rest of the realm.
So if you own W, X, Y, and Z, and they loot W, X, and Y, Z is still gonna love them. Even if you declare hatred and "whip your peasants in a hatred frenzy against them".
Sure, you can go do diplo work to reduce sympathy, but it's a painful process, especially if you have a large realm or many regions.
I would get this feature if it was the result of diplo work to increase sympathy significantly, but as it is, it just seems to appear from default values. Even if the effects are tiny, the text that is presented sends a really bad message.
