I think that Chris Hein's argument that it's about retaining a weapon is persuasive...but in addition to having no real experience doing that kind of live practice, I'm also suspicious of saying that techniques will magically start working better than judo/BJJ if you put a knife in one person's hand, or strap a sword at your waist. It seems like even if they're optimized for weapons, they should function empty-handed.
Well I don't think it works better then judo/bjj. In fact I believe that the roots of judo/bjj/aikido share their weapon orientation. However judo and bjj have been developed over time, through competition to make unarmed systems. They dropped the techniques that are really low percentage in unarmed fighting. Like wrist locks, shihonage, etc.
Now the reason Aikido retained these techniques is simple, there was no unarmed competition. No one ever found these to be low percentage unarmed techniques, so they kept them. The trouble with this, Aikidoka never learned how to actually apply the techniques, and what they were for, they never practiced them against resistance.
Now why are these techniques higher percentage with a weapon? The answer is simple, because of the necessity of controlling the weapon hand. In an unarmed fight, the striking hand can simply be checked, or kept in tight enough to not generate power. However a knife can generate huge amounts of power in a very tight space. In order to keep a knife from doing damage you much tightly control it (ie wrist grabbing). Now if you have to hold the weapon hand, in order to stay alive, your focus, and technique choice is going to be different then if you could skip holding the hand, and go to holding the core (unarmed fighting). So things like shihonage, sankyo, kotegaishi etc. are now higher percentage techniques.
We can chat about it all day, but the best thing to do is try it. Get an Aikido buddy, have have him try and stop you from "killing" him with a wooden knife. Notice how often he grabs and holds your wrist. Notice how often you get then the positions that Aikido techniques pop up. You don't have to take my word for it, just try it, you'll see. And anyone who wants to is always welcome at my dojo. We'll train together and talk about what we find out!