I think the instigator rule, ostensibly designed to curtail 'sideshow' fights, ironically had the effect of relegating fighting largely to goons, who would carefully coordinate fighting opportunities according to an arcane formula so as to avoid being instigators. (Well, except for Laraque, who just politely opted out every time )
The main reason fighting has withered seems, however, to be advanced stats, which demonstrate pretty conclusively (or so I understand) that teams with goons on the ice surrender way more scoring chances, etc.. Once teams realize that, they start insisting that *everyone* on the team be a quality hockey player. So much for the goons.
Add to that the concern over concussions. Even though fights often don't cause them, it's still hard to celebrate watching young men receive repeated and intentional blows to the head. I used to love hockey fights (as well as boxing), but now they tend to make me wince, knowing the damage that concussions do.
Finally: I'm not seeing this huge spike in cheap shots, myself. The cheap shots were always there, and the kind of unbelievable punishment that used to get doled out, especially in the slot, now tends to get called by officials. Meanwhile Scott Stevens-style headhunting has been cracked down on. I think fighting is a 'solution' to a non-problem, basically.