No it doesn't. Penalize dirty shit with lengthier suspensions, it'll be much more effective.
Care to elaborate?
Anyone bringing up the old discussion, already discussed and dismissed many times, of banning fighting in NHL hockey is showing a blatant lack of understanding of the the fundamentals of NHL hockey.
In NHL hockey, the ice is smaller and the game is about competing for possession of a single tiny puck, competing physically for a single area/space where the puck is or might go, or competing for a space where one might score or prevent a scoring chance, there is a lot of highly competitive, physical battles that are fought. Eventually someone will win, lose or tie in the dozens and dozens of these battles that take place each period, each game. In fact, winning these battles is pretty much the main point of the game and the score is usually there as an indicator of who won the most (or at least the most significant) battles on the ice.
Inevitably there will games where one team wins several battles consecutively over the other and achieves a significant advantage in momentum and morale. And if that momentum is not stopped, the game outcome will inevitably be against the other team and in order for that other team to have a chance, they must do something drastic to halt that winning team's momentum.
When this situation happens, that's normally when fighting occurs in the NHL and since the time the players got together, both informally as a camaraderie of fellow players and formally to form the NHLPA, they ritualized the process and came up with "fighting". NHL "fighting" is bare-handed with fists, one on one and both combatants will be penalized in order to cool down. Other players, no matter how angry or frustrated, are to watch and cheer from the sidelines and let their frustrations and energy be channeled, then dissipated by the two voluntary combatants. (no foreign objects, no finger gouging of eyes or mouth, no head butts, etc.) Fights last just a couple minutes and end, when the two combatants inevitably run out of breath.
The ritual formed in order to create an understood situation for both teams and prevent two situations: 1) players on their own won't use the possible deadly weapons in their possession on each other including stick blades via hacking, broken stick shafts via spearing, skate blades via slicing, etc.; and 2), all of the players going into a free-for-all.
Basically if there is no fighting, the alternatives are basically players literally killing and maiming each other and it can spread to overall situations that will be akin to rioting, similar to soccer. Imagine if soccer riots turned into situation where each rioter got a hockey stick and two knives on their feet.
Even the audience appreciates these battles as they are, in a way, gentlemanly in their one vs. one voluntary combat, which is intuitively understood as two guys, representing their teams, duking it out fairly and intensely.