As an 'outsider' to hockey, it seems to me the issues with the league relating to dirty hits and fighting come down to:
- players not caring about hitting each other high or dangerously
- the league not caring
- it's very hard to suspend or meaningfully fine players (NHLPA influence?) and there's no rules, or even useful and clear guidelines on when suspensions should apply
- there's no penalty less than 2 mins, so a lot gets let go because it doesn't 'deserve' to put a team 1 man down
I grew up playing Aussie Rules and Rugby, two sports that I believe have a similar level of physicality, toughness and intensity to hockey (which I've also played, but I dind't grow up with it), yet neither sport has anywhere near the levels of headshots/high contact that you see in hockey, and fighting is almost non-existent. Most 'brawls' are a lot of pushing and shoving, but punches are rarely thrown and almost all contact is below the shoulders. When I watch a hockey game it astounds me that immediately after a whistle gloves and sticks get right into faces, is it because of the armour being worn? In other codes hitting someone in the head/face is seen as 'weak'.
Both other sports penalize incidental high contact with possession and territory advantage to the other team which can't really be done in hockey (and offensive zone faceoff wouldn't suffice), but there needs to be some kind of disincentive to stop players from getting their hands and sticks up all the time. 1 min penalties seem like they wouldn't work (and you'd have a penalty parade until players adjusted), but there needs to be something that causes players to stop and think.
On suspensions; and accidental (arrived at the contest slightly late and hit another player high while going for the ball) head high contact will likely see an AFL (Aussie Rules) player suspended for a game or two (which increases with each incident they're involved in), and as they only play 22 games a season, most players try and avoid this. 1 or 2 games in an 82 game season isn't a deterrent (the 2 games mentioned above would be a 7 game NHL suspension based on % of season), especially when the PA seems to argue almost every decision. Every AFL game is reviewed for incidents and the players can be 'reported' during this review and then face suspensions based on published guidelines that are linked to the rules (the system isn't perfect, but it's not bad). I know that there's a lot more hockey games in a tighter timeframe, but the NHL also has a lot more resources to check the games, identify high/illegal hits and suspend players.
If you could get buy-in from both the league and PA it's something you could stamp out pretty quickly with the right enforcement and deterrent, with the only real pushback coming from past players of a certain type and the "go watch figure skating crowd", I'm just not really sure that either party will care enough until a few in-ther-prime stars actually have to quite due to head injuries.