I think that's about the same percentage of aikido that, in the past, you've suggested doesn't work. Maybe more people should train with weapons more often.
The men who developed the body of techniques of which aikido movements come from were not that interested in unarmed combat. They were required by law to carry swords, and used other weapons as well.
If you look at more open empty-hand fighting, like UFC, the techniques of BJJ are low percentage. Most of them have their roots in the same period of Japanese history.
Now, let's look at the most successful empty-hand techniques: wrestling takedowns, ground and pound, boxing/muay thai, chokes, blocking punches/kicks, and using the guard to minimize the effect of strikes. If you face someone with a weapon, these techniques will cost you. Even if you "win" you will likely be severely injured. You have to respect the weapon. You have to isolate and control the weapon arm. The weapon creates the necessity of the "lower percentage" techniques. If you are using the weapon, your best bet is to maintain control of it and continue to use it.
There's no magic to it. It's still quite difficult to use the techniques against a resisting opponent, but you will begin to see the reasoning behind it. But why take my word for it. I could be all wrong, so try it yourself. Get a tanto and some training partners, use BJJ/judo, and be honest about the "cuts" and "stabs" (I recommend striking below the neck only) you would have received and what probable effect they would have. Remember: a 3-4" folding knife can be extremely lethal.
There is nothing wrong with learning to hit hard, or grapple; they are excellent skills to have, and if you love a particular art, by all means, practice it, but it's wise to remember that the scope of physical conflict is much greater than 1-on-1 empty-hand fighting.
So I ask this question, If aikido only works when defending weapons, why do we not just train always with uke using a weapon? When I practice playing 9-ball, I always use a pool cue and balls. When I practice swimming, I always use a pool, when I practice fencing, I always use a sword. But when I practice aikido, 99% of the time, it is punches, overhand strikes, and those yokomen strikes, wrist and lapel grabs, etc. Then every now and then we break out a tanto or jo and defend against that (I've done this maybe 4 times in my time in aikido. Oh and we do a jo kata every few months or so.
Most video's I see on the net are also empty handed. So again, it seems to me, that it is a poor way to train to defend weapons without actually having someone attack you with a weapon. In fact it could even work better for you, give a guy a rubber baton to attack with and he is going to commit to his strike more. The reasoning is because he won't have the mental block that hitting you is going to hurt you. So he can just swing for 'the kill'. The same is true with rubber knifes. It seems to me that giving noobs weapons to attack you in this manner would remove the fear of hitting you. Thus they would commit properly and allow us to train what we are trying to train.
The last thing I'd like to cover is this, knife defenses are a joke. Seriously, I think it is laughable every time I see a knife defense. No one will ever, ever, ever attack you like that with a knife. Not in prison, on the street, in the woods, in the ocean, etc. Well ok someone will attack you like that, but only if you hand them a knife and tell them to attack you like that and you are in a dojo. A real knife attack is going to come out of the blue, probably a opening sneak attack from behind. You won't know the knife is there until its stuck into your back. Then as he pulls it out, maybe you can defend yourself. But that is just my opinion from watching videos with knife attacks on the street and in prison. They usually walk up real close, pull the blade and stab short fast repeated blows to the midsection or face. No lunging, chopping, etc. The distances is defiantly not the range most knife defenses train. Anyways, that's just my pet peeve. I was impressed with my instructors defenses against the baseball bat swing with a joe. But I've yet to be impressed with any knife defense work I've seen, save the work I've seen from the dog brothers.