Playing Diplomacy (the board game) is not for everyone. It's a game where you must eventually stab every other player in the back, if you want to win. Thing is, everyone at the table knows it going in. Which is why some people don't go in.
An RPG session that features unlimited PvP doesn't necessary end that way. Some of the PCs could form alliances and honor them. However, if any devious or backstabbing plan is allowed, then everyone has to go into the session ready to accept it as part of the game. Really accept it--not lip service. For one thing, it allows the players to create a little extra detachment from their characters.
I've played absolutely no PvP, very constrained PvP (my preference), mostly PvP with no holds barred scheming and misdirection but no outright lethal confrontation, and wide-open, anything goes PvP. The last two are a very acquired taste. Even players that have gleefully jumped in and had a blast all wanted something more team-oriented after such a short campaign. I've even done it without the separate sessions: A handful of note passing on preset plans and the target players being the audience for what was about to be unleashed on them while acting as if they didn't know who was really responsible. Sometimes even rueful admiration for what was being done to them. You really need detachment to play that way, which is certainly not for everyone.