Triple D, welcome to TFL!
I'll be the semi-devil's advocate (just to keep this from being a thread where everyone drops in with a "one-liner of wisdom" it's been good so far), gryphon hit the nail on the head when he says it's about the damage. An open hand gives you the option of drawing blood whereas a knife makes it pretty much a necessity with a motivated attacker. As far as I know, police are given asp, baton, mace, and H2H training... not knives. There are times that less force is better.
Also, I notice most responses are critical of the few items I put on "my" list... please realize I don't remember the items from the original. One thing I imagine would be on the original would be the ability to throw and dynamically grapple. I realize there are isolated examples where you would be able to throw someone such and such a way (or basically forcefully shove) even with a knife in hand... or even grapple in a specific position- but from what I've seen, it doesn't seem possible with a knife (or any other object) in hand. Throws are a good way of controlling groups whereas a knife tends to crystalize their actions into teamwork aimed at getting rid of that knife (just my observations from "reality" TV like Police Videos, MaxEx, etc.)... finally, if a knife is as useful as open hand, shouldn't more martial arts emphasize knife use more? Granted, a lot of it has to do with tradition, but how does it turn out that so few seriously deal with it? Finally, there are legal considerations, IMO... unless your fists are registered as deadly weapons!
One other note, please don't take the "dropping the knife" literally for discussion purposes... perhaps the decision whether to sheath or unsheath?