I recently spent an evening around a campfire with a group of coworkers and the knife discussion came up. One of the guys had a big 1/4" thick, 7" blade survival style knife and we had loads of fun giving him crap about it. His response was one of pure shock that we all didn't have our own 7" blade bowie knives. He said, "I thought everyone brought a knife camping". We then spent the next couple hours at the campfire watching him baton firewood into smaller firewood, make fire-bows, etc. In short, his knife provided a lot of entertainment for about 15 people for an evening. :) On a serious note, he'd also done a lot of survival studying and practice, and if you were in a real wilderness emergency, would be the kind of guy to have along. He liked to think outside the box.
I think in our day of cuben fiber tarps and freeze-dried, vacuum packed meals, it is harder for us to imagine the uses of a knife for survival. Less than 100 years ago, when jogging to your car for a bail-out of the mountains wasn't an option, a knife was an essential part of survival. I think that is the key to whether a knife is "essential" or not. Can it be replaced with other items in the event you do need it?, and how likely is it that you'll need it.
Personally, I like a small knife as it is one of the most "multipurpose" items in my kit. I thought that's one of the things we try to go for in BPL, is having items that serve more than one purpose. It came in super handy for me when I needed to use a flint striker because my Bic lighter was frozen, when I needed to cut cord, or make kindling, etc. And yes, I use it to clean my fingernails and dig out splinters, pop blisters, cut bandaging materials. None of those are theoretical uses, those are all things I've done with a knife on camping trips.
The answer is different for all of us, since we have different styles and needs. An item for protection alone, like a firearm, can be tough for me to justify; It is solely based on a highly unlikely scenario, weighs quite a bit, and is a single purpose item. A knife, on the other hand, has a multitude of uses, is lighter weight, and is a super easy answer for me.
Some folks snicker at the "over prepared" hikers who plan for worst case scenario. For me it is a balancing act of emergency preparedness, comfort, and light weight. I think that going to either extreme can be a bad idea. If you're one of the lucky folks who have never needed better raingear, a sturdier tent or pack, a knife, or a first aid kit in the back country, then I'm genuinely happy for you. Many of us are in the same boat. Many, but not all. After spending the past 16 years on SAR, I have met my share of folks who suffered from having too minimalist a strategy. ;)