So, on console, traitstone drops are tied to kingdom for challenge & quests.
But they are NOT tied to kingdom for PvP battles. You essentially just get random drops.
In my opinion, hitting “new opponent” 10 times, or 20 times, in order to get the kingdom you want, is unfun. PvP should be about the teams you are facing, not anything else. When home kingdom also set your mana bonus, you could see by the home kingdom what sort of troops they might be using. But now that home kingdom & banners are distinct, there is really no interesting strategy there.
The reward for PvP is the glory, the rank, and the complex & sophisticated defense teams people set up. I think that thinking of it as a source for traitstone farming is not the mindset we want to encourage.