Once read an article about deer hunting that was based on a similar question the article was entitled "Touching Wild" and was based off of the first time a hunter gets to touch the antler of buck he/she just killed. Very good article and I believe it has the same answer in the end, its primal, were hardwired for it, basically its in our DNA. It taps into something so deep in our psyche we don't even realize it nor do we understand it. It goes back to our long ago ancestors with the tribe roasting mammoth meat, over a fire on the open plain under the stars, etc.
A lot of people mention its man's earliest tool and it is, it is also still around although modified, still useful, still necessary and if all else fails it is still essentially to our survival and is really the one tool would need to not only survive but thrive. Think about that for a second, I mean sit back clear your mind and really invest a few minutes of time thinking about what that means and all that it implies.
The knife it like the alpha and omega of tools it got us started, by developing cutting tools modern civilization flourished and has made beyond tremendous gains/advances, and if it all fizzles out tonight, we'd be back to the knife where we started.
The question you ask in my opinion is almost unanswerable as its too layered, varied and complex. If early man had not invented or accidentally discovered the cutting edge (knife), this grand experiment would have turned out much different and humans more than likely would have died out long ago. We sure wouldn't be where we are today.
Dang, am I over analyzing things again, my wife tells me I'm bad about that, sorry.