I’ll also say that you really do have to separate out two concepts:
In-character conflict, which may be between player characters
and
Player vs player conflict, where the PCs are mainly proxies for beating ‘the other guy’ on an ooc level.
I’ve had far more rich, rewarding, and intense conflict and competition between characters when there is no OOC masque, when players OOCly communicate about stakes, outcomes, desires, than when that conflict is treated as a competition between players. Like, I’ve had intrigue and espionage plots/scenes that could only happen BECAUSE we were talking OOC and cool with things happening. Also, being able to chat with people OOC about how we see this conflict helps me identify at a much earlier stage if this is a player who can handle conflict, or who it’s just not going to be fun trying to have these sorts of scenes with.
A secondary issue is something I learned as a newbie GM and which has never steered me wrong in the days since: “You can’t solve an OOC problem with an IC solution.” If the problem is “this player is playing their character in a way that makes the game unfun for other people”, then punishing/beating up/demoting/killing their character is never the solution. Having an adult conversation with them OOC about the effect their play is having on others’ fun is, and if that conversation doesn’t go well, then removing them from the game is.
Killing someone’s character because you’re OOCly annoyed with the player is one of the ways PvP gets real toxic, real fast. It’s not ‘policing the community’, it’s just taking your frustration out on someone who you usually know that you can beat and have often taken every measure to make sure that fight is as one-sided and humiliating as possible, because you’re there to ‘teach the player a lesson’, not to have fun with them.