I think your violin example misses the point.
What violin example? If I recall correctly, I clearly stated a vocalist's example.
Boxers, and grapplers isolate techniques and work them individually or on a bag too. But your violin example concerning kata would be like trying to learn to play without a violin. You can moves your hands in a violin playing motion, you might even get some benefit from it but to say it's superior is not true.
Where did I say that it was superior? I simply stated that it's a proven way that helps you perfect your techniques to the point where teaching someone advanced application becomes much easier.
Furthermore, your example of the air violin is not valid in this case, since performing waza in a kata is performing the actual technique, and there's a premium on proper bodily mechanics, conditioning, timing, awareness, etc., all of which are vital to a martial artist. Your air violin example isn't actually playing the violin, nor is it developing any kind of technique or actual skill, which is why it's not a valid comparison, since the techniques of Karate performed in kata are certainly valid.
If you said that you saw a dojo where people were simply flailing around their arms and legs in a totally random motion, then I would agree, but this is clearly not the case.
A better comparison would be a violinist using the proven and tested Kreutzer exercises to strengthen his fingers, develop better timing, develop better intonation, precision, accuracy, and to be able to train brain to work more optimally. Someone who has shown that he can perform all of the Kreutzer exercises with a high level of proficiency can certainly be taught to tackle on any number of advanced concertos.
If you're in no hurry to learn to play the violin go ahead and "ghost" violin in the air, kata is the same thing. I'm not saying it's useless but if it were the superior method of training to learn fighting skill they'd be doing it in the ring or to prepare for the ring.
I simply disagree with you and your assertion. I've seen the value of kata, and well-respected organizations the likes of the JKA, along with Kanazawa's SKIF and Okazaki's ISKA, have done exceptionally well using these methods.