Yes, the fighting is part of the tradition of hockey. On a practical level, a player is less likely to make a dirty play against an opponent's skill player if he knows that an enforcer will be looking for him later on to fight. Fisticuffs are the tool that the players use to police the game.
The reality is that for many fans of the sport, fighting is an integral part of a hockey game. Indeed, for many a professional player, fights on the ice are anticipated. Although fighting should not be encouraged because of the physical risk presented to players, on the professional level, an outright ban on fighting is unnecessary.
No, fighting should not be allowed in hockey because it encourages violence as a part of sport. The game of hockey has rules and regulations, and it should be played according to those rules, just like any other sport. Players who fight exhibit poor sportsmanship and serve as inferior role models to children who watch the games.