It influences how another team plays against you.
For example, if I am coaching against the Canucks, I know Green's philosophy does nothing to protect star players like Petey and Hughes, and that the team doesn't use hitting to advantage (a specific example would be what Jake can do - when he is aggressively hitting on the forecheck, other teams D often cough up the puck even when Jake is not on the ice; unfortunately those games were few and far between and appear to be in the past).
I also know that the NHL reffing is a dinosaur institution of morons. (sorry morons, I meant to say idiots).
Knowing this, my gameplan is to have players run Petey and Hughes, can-opener them (Mathesen), get tangled up with them mid-ice (Koktaniemi), and constantly give them punches and head shots behind the play (watch some of the hilite vids made of the abuse Petey took behind the play last season).
I do this knowing the Green as a coach doesn't protect his star players, and the Canucks as players rarely do anything about it. It's a no lose game plan, given NHL reffing. Odds are that penalties will offset as retaliation gets called as much as if not more than instigation. Look at what happened the previous game with Hogs. WPG is going on the PK, so they get rough, and instead of it being a 5 on 3 for the Canucks, it's even strenght. effing NHL refs. But that's the game as it is right now.
So the proper response is to have your speedy forecheckers finishing checks - yep, they are taken out of the play, but the opponent they hit it also taken out of the play, and hopefully bruised (sorry, it's a grind, that's hockey) and also next time they cough up the puck earlier. And if someone looks at Petey or Hughes sideways, you hammer them. And then hammer them again. Or straight up fight them. The effin NHL refs are only going to call a fraction of it, and more often than not you will get even up/retaliation calls where you don't get a man disadvantage.
Done in fits and starts, it doesn't change the opposition game plan. Done with strategic foresight and executed consistently, the other team coughs up the puck, and they stop taking cheap shots at your players.
I lived through it for a decade, back when hitting from behind was not just legal, it was required - you would get chewed out or benched for not finishing checks including those checks. Hitting from behind has thankfully gone the way of the dodo, but as long as the dodo's are still in charge of NHL reffing, that's what it takes to have success over the long term grind that is NHL hockey.