But they only like it because it's been around for so long. There's absolutely no reason for it. And if people stop watching games because they remove fighting then those aren't real fans. I'm not saying you're not a hockey fan if you like fighting, but if you actually stop watching hockey all because they remove fighting, then those aren't real fans. So, yes, they might lose some "fans" if they take fighting out of the game, but I don't think they'd lose hockey fans.
The only legitimate reason to keep fighting, is to prevent players from taking rasher actions with intent to injure. If you can't fight, players are going to look for another way to get their revenge. I don't care for it as entertainment. Even fighting sports have padded flooring and gloves to reduce the potential impact from someone falling on their head or taking bare knuckle punches. If they want to stop the game, drag out a mat, take off the skates, and put gloves on before engaging in a fight, then they can keep it for entertainment.
As for the "legitimate" reason to keep fighting, revenge culture exists with or without it, so that argument is thin to begin with. Any intent to injure has to be punished with extreme prejudice. Questionably "accidental" injury to an opponent should be punished progressively. In order for that to happen, there has to be strict application and adherence to the rules. That means calling EVERY penalty until the players learn and evolve. Facewashing, slashing, shoving after the whistle, even excessive body checking, all need to be called. The game would be significantly different and it would take years to breed those behaviors out. It's never going to happen. The league doesn't want it, traditionalists don't like it, and fans would mostly be against it as well.
Imagine 10 years of games, where 50% or more was spent on special teams and double digit scores were a regular occurrence. That's what it would take to get fighting out of the game and you would reduce injuries in the process. Newer generations would grow to a game where skill, speed, and discipline, were the key components, and they would adapt and reinforce those elements. The NHL however, wants to continue paying neanderthals with sticks millions of dollars to endanger the livelihood of the players that people actually want to watch. For every one person that tunes in to see a player like Reaves, there are thousands who are more interested in seeing a McDavid or Crosby, so it makes sense to adapt the game in a way which further features those skilled players.
If you're getting paid hundreds of thousands of dollars, even millions, to play a sport AND keep your temper in check, and you can't do it, they should throw you out on your ass. All they have to do is decide that keeping your temper in check is a condition of your employment, just like almost every other business in the world with a respectable HR department.