If you want to make enemies, try to change something.
Well, I see nothing wrong with regular PvP that is seperate from TC and requires no gang/supplies. The danger is that if you just left something like the Cathedral even trunning 24/7 it would quickly get boring because there is nothing really to achieve. An endless cycle of killing for no reason can only be fun for so long. Allowing it to be available regularly so it remains a novelty and well populated would seem to be the best way to go about it.
If there was multiple pvp areas like a hth arena where you could compete for titles in the pipboy and have bets placed on it
or a large outdoor map with 2 sides for team vs team dm it would just add things to do without upsetting the balance of the rest of the game as well as making it more open to casual gamers.