According to hockeyfights, we had three players with 5 fights, and one player with 6. I'll let you guess who the player with 6 was. (Hint: He won't be playing for the Bruins until at least 10/25...and probably never.)
http://www.hockeyfights.com/leaders/players/1/reg2016
If you want a list of the people in the NHL that this would effect, here we go:
http://www.hockeyfights.com/leaders/players/1/reg2016
Good old Campbell's up there with 8 fights. Note that these don't deduct for the "instigator", but my estimate would be instigators make up somewhere between 10-30% of fights...certainly not more.
For the "soft" Bruins, this doesn't change a thing. But there are 12 players with 8-9 fights who would be in the danger zone, and 4 players who would be suspended for a game. The leader, Cody McLeod, had 12 fights, so he wasn't THAT close to the 2 game suspension.
NB: I have no idea how reliable hockeyfights is, but I read something where it says it's considered a fight when (at least) one player is charged with a 5 minute major. If anything, it sounds like an overestimate. Either way, there's an average of 1 player per 2-3 teams who's in danger of a 1 game suspension - not terribly game-changing.
I can definitely see how this would make sense at the AHL level:
http://www.hockeyfights.com/leaders/players/2/reg2016
They have 22 players with 10+ fights, and one with 20. It gives credence to the "AHL goon" stereotype. Their first liners are trying to show grit to make it to the NHL, and their fourth liners are more goony than the NHL fourth liners.
EDIT: One final thought that I came up with after this stirring in my mind for an hour or so. This will turn a skilled player-fighter (think Marchand/McQuaid, not Rinaldo/Randell) into a virtual piñata in late March if they rack up 8 or 9 fights and their team is in a playoff race. A player with 4 fights will be eager to go at someone with 9 who's scared of getting #10.