it would have to involve an action well after a play and would have to result in or potentially result in a serious injury. Obviously any player who leaves the court or field and assaults a fan, that's a law enforcement thing and not part of the game.

I wouldn't want criminal charges against the basketball player in that video, but I would expect the school to at the very least kick him off the team. If that was a pro player a massive fine and suspension.

The hockey player who spears a guys throat while skating along during a break, that would be something to consider criminal charges (used the stick as a weapon, absolutely not part of game play, potential for serious or life threatening injury).

My concern would be lawsuits being filed for plays that are borderline part of the game (blowing up a receiver on a crossing route, hard check from behind into the boards, hard foul on a guy going in for a layup).

Obviously there are grey areas, I would expect most things that are remotely part of the game (even though against the rules) should be handled by the game, not by law enforcement.