As a member of Mitsunari Kanai's lineage, I have asked myself many of the questions covered in this thread, but with regards to iaido rather than kenjutsu. My main teachers were all students of Kanai Sensei and he is the source of most of the aikiken forms I learned. My teachers all trained in iaido with Kanai, though I have never taken it up. He touches on many of the topics touched on in this thread in this interview:
On the uniqueness of O-sensei's sword practice:
" Haga Sensei told us that O-Sensei's sword technique was something "different", and he did not understand it well. He seemed to feel that O-sensei had something special but he didn't know what it was. "
On weapons training in aikido and training with a real sword:
" In Aikido, when you advance to higher grades, i.e. second-kyu and above, you learn Buki Tori (techniques to take away weapons). However, generally speaking, students do not actually learn how to handle weapons. Students are not taught how to attack correctly with a weapon or how to cut with a sword. So in that sense, it is good for students to experience using a real sword. If you actually practice with a real sword, and understand how to cut with a sword, you know how to attack with a sword. Unless you know how to attack with a weapon you cannot, in a real sense, do Buki Dori, especially Tachi Dori. In this context, I think there is a relationship between Iaido and Aikido."
and " It is easier to concentrate your mind when doing suburi with a real sword. In this sense, Iaido is really good. To do suburi with a real sword is very healthy for the mind. I really like it. Similarly, it is easier to concentrate your mind, or unify your body and mind, when you are holding a real sword. You concentrate your mind in the tip of the sword.
There is a difference between doing suburi with a real sword and with a bokken. When doing suburi with a real sword you become aware of the cutting line of the sword edge. This sharpness makes your concentration much more sharp."
And on the principles of aikido and how they transend specific forms:
"In the past, I viewed other Budo such as Judo, Karate or Kendo as entirely different from Aikido. And I used to feel that it was odd or not proper to do them together in the context of Aikido. That was how I used to look at them. But once I better understood the theory of Aikido, I did not feel so reluctant. For example, if I apply a Judo technique, I apply it based on the theory of Aikido. To me, it is an Aikido technique. And when I use a sword, I do not feel I am doing Kendo. Rather, I feel it is a part of Aikido and, moreover, that it is already contained in Aikido. Recently, I increasingly have felt that kind of freedom and flexibility about Aikido. So in this sense, I think you can say Aikido is the total Budo.
I hesitate to say this because I mean it in a very specific way, and this idea can be easily misunderstood. Before one really understands what Aikido is, one should never mix it together with other Budo such as Kendo or Judo. This idea has nothing to do with mixing different martial arts together.
A correct understanding of Aikido's fundamental principle, how it includes everything and transforms everything, requires great subtlety to appreciate and long and hard work to achieve."
My conclusion. Maybe I should consider doing some iaido to better understand the sword. Especially since I now have the responsibility of teaching the weapons class at my dojo. Don't know where I'd find the time though. Maybe it doesn't matter as long as I try to embody the aikido's fundamental principle. Too bad he didn't go into what he felt that was in this context.