There is never going to be consistency from game to game. Different officials see thinks differently, have different levels of experience, take different angles (especially if they had to avoid the play beforehand), focus on different things based on their experience, etc. What they can control is the extremes on both ends. Truth is, during the regular season it does not matter much. What is more important is consistency by the individual officials during the game.
If a team sees that one of the referees for their January 17th game is Lipshitz, and they know Lipshitz historically calls a tight game, they adjust. If they have McGooligan on January 20th and they know he has historically been more inclined to let them play, they adjust. It's that way in all sports. What you don't want is Lipshitz or McGooligan bucking their own trends and become random when they are on the ice.
The consistency from game to game in the playoffs is more sensitive.....but the league controls that by who they put on the ice. It is much easier for the league to control the difference between the extremes when they are selecting a smaller pool of officials.
The other thing people do not widely recognize is that all leagues (at pretty much all levels) issue "rules clarifications," "interpretations," and "points of emphasis" all the time, and we generally do not hear about them. If you find yourself asking how none of the officials ever calls xxx, it is quite likely because they have been told not to. The NBA is traditionally the worst at this, largely because some of their points of emphasis would ruin the integrity of the sport (and probably have). MLB once "interpreted" the strike zone, which was plainly defined at the time as from the armpits to the top of the knees, to be the belt to the top of the knees.
When the league went to the four-man system, it was sorely needed. The game had gotten much faster and the athletes much better, making the idea of one referee watching the whole thing, including the play away from the puck (while telling him to watch the puck) impossible. The game is now faster still, and there really is no room to add anybody else without them getting in the way more often. So now we have two guys able to police the action of 10, plus watching the puck, and watching the area around the net. Some of that can be resolved by broadening what the replay official can look at, but be careful what you wish for. I really do not want them stopping at every frozen puck to talk about something.
To give the NHL officials some credit, they are the best of all the sports and what is termed "preventative officiating." You hear it all the time. "Let him go," "don't hold him," "get your sticks down," etc. Players generally appreciate that a lot more than having the guy just raise his arm right away.
And the "equal and opposite reaction" to calling everything is that they will also start calling things that didn't really happen because they are basically told to err in that direction, or things that they expected to happen. Expectation bias is the enemy of any official in any sport. You can ask the NFL how that worked when they informed their officials that anybody failing to call an illegal hit on a QB would be dealt with. They still have that mess to clean up.