Overall hitting may be down sure - because the whole game would change. It'd turn into a skills competition where no defending teammates/etc could happen. Obviously stuff would go down.
However, HARD hits - dirty hits - etc would most likely for sure go way up if players feel that's the only way to release frustration.
In pro sports - players will go as far as they can. Whether that's taking supplements, pushing boundaries, using rules, etc. Right now when there's a lot of frustration a player knows fighting could still be an option and a player will fight when tensions rise as that's how things get handled. That's why Wilson got into a fight in this game. If he didn't get in a fight you can bet your ass he'd of got checked or hit super hard/border line dirty/or straight up dirty. Players will go as far as they can when emotions rise like that.
This is the NHL - not a inferior league.