Zen & Iaidō
It is important to understand that doing Iaidō and doing Zen is not necessarily the same thing. They are closely interrelated, but it is a mistake to think that just by practicing Iaidō that you will achieve Zen satori (enlightenment) in short order. Iaido is one way among many to approach the training of Zen and to describe iaidō as "moving Zen" is probably not entirely accurate.
Training in Iaidō is a way to help you understand the truth of what surrounds you. The training is a metaphor for the variety of situations and complications we all experience in our life, and it is important to be aware of the parallels that Iaido teaches us. Many aspects of dōjō etiquette and practice can be applied to your everyday life. For example it is always good to be aware of what is around you and your relationship to those people or things. This also helps you to choose the best path of your actions. This is Iai and the Zen of Iaidō.
When you do Iaidō you still need to do the kata with the purpose of the kata in mind. iaido is not moving meditation, Za-zen or anything else; Iaidō is Iaidō. If the purpose of the kata is to kill the enemy then this the the feeling that you need to be doing the kata with. In Mugai-ryu, the purpose of the kata is generally not to kill the enemy, but instead the person attacking you, dying on your sword is a natural consequence of his actions and choices. You still need to intend to dispatch him nevertheless and give him a quick and relatively kind death.
At the higher levels of Mugai-ryu Iaidō and jōdō, the purpose of the kata is to try to avoid killing your attacker and then further on to try to avoid them attacking you in the first place. In this case, this is the attitude that you need to do Iaidō with.
Zen in these cases is a natural by-product of doing Iaidō, if you are aware of the meanings and nuances in this respect.
An interesting parallel is with Chanoyu (The Tea Ceremony). The whole purpose of Chanoyu is not to drink tea, it is also a type of Zen. But if you don't approach Chanoyu with the mind of making a good cup of tea for your guests then the whole meaning and link to Zen then disappears. If you rush through the movements, use shortcuts and put in a tea bag, you will get a drinkable cup of tea, but there will be absolutely no learning gained with respect to Zen, and it will no longer be Chanoyu.
This is exactly the same with Iaidō and other Zen kenjutsu. if you don't focus on what you should be doing, where you should be cutting, what the next attacker is doing, and what his friends are doing, as if it were a real sword encounter, then you will lose the sense of Zen.
Conversely, if the thrill of a real sword battle is all that you seek and you are not sensitive to the metaphorical nuances of what you are doing, then you will also fall further from the path of Zen. Iaido is not for the purpose of learning how to kill people with a sword, and if this is the only thing you focus on, then you are not only not doing Iaidō, you are also not learning anything with respect to Zen.