At one point, PvP was seen as the solution for community problems. Yes, the developers and moderators could take action against problem customers, but nothing says “you’re fired” quite like killing someone and setting fire to all their stuff. You can also see why giving players that power could be problematic, for example in the officially non-PvP Sims Online where mafias would extort resources from new players under threat of mass-downrating them as griefers. In practice, apart from A Tale in the Desert, most recent games have made the consequences players could impose on each other small, avoiding having players driven out and instead implementing things like automatic group-finding that minimize any social consequences for sociopathy.
In an environment of anonymity, low consequences, and high competitiveness, PvP communities are often quite toxic. I have known people to use trolling as a form of crowd control, as a quick comment or two can leave a target typing for minutes and agitated for an entire round.
One approach occasionally in use is asynchronous PvP. “Asynchronous” means “not at the same time,” so one player sets up a computer-controlled challenge and other players face the challenge. Elements has an an arena, so the computer controls a player-built deck. Marvel Puzzle Quest remembers which team you last used to attack and controls it as your team for defense.
This converts PvP to another form of PvE. In many circumstances, there is not even a way to tell which opponent used your defense as a challenge target. You might talk smack out-of-game, but in-game there is no direct interaction with your PvP target.
The advantages of player-built, computer-controlled teams are known. Some strategies work better or worse in the hands of a computer, and building around the computer’s AI is a skill in itself. Tricks tend to work less well because the computer is not in on the trick, but items needing precision application can safely be left in the hands of a pilot who “thinks” in micro-seconds.