The bolded may be true, however those are tournament style formats, same as the old Canada Cup, or World Cup, and those are a national team make up, so your typical "fighter" won't likely be on those teams. You can't compare that to regular season NHL (CHL), or even playoffs. Also.......fighting isn't allowed in NCAA, and it's also not allowed in any league, but it is penalized. Fights happen in the NCAA, but they get a suspension for the next game, plus they are mandated to wear full face shields/cages - kind of a deterrent itself.
I 100% disagree with your last statement though (getting rid of it overnight....). Fights serve more than just a self policing aspect of the game. We've seen it many times (although not so much recently) where a fight can swing momentum in a game. It can also serve as a release valve for tensions in a game - hence Simmons wanting the fight towards the end of the last Winnipeg game. In fact that last game against the Jets played out exactly how I wanted it to. Win the game, and get a 3 or more lead with enough time to take care of the business from the last game. Still would've been nice to have that last fight though, but the refs decided differently. That would not have been the case even just 3 or years ago.