I see I've missed a bit while I was away. Other people have already brought forward some of the points i was going to make, so I'm not going to repeat them.
Paul, I have to say that your "learning to drive a car comparison" seemed a bit off... according to the definition you give here, nobody above 5th kyu would be doing any more kata.
But let me just recycle the "car" analogy to clarify my own point of view...
First, you go sit behind the wheel, and your instructor will point out what everything is, what it's for and how you use it. This is the wheel, it turns like this, this is how you change gears, this pedal is the brake, etc. In a car, that takes about ten minutes. In aikido, we start by explaining and showing a newbie some of the basics: this is kamae, this is tenkan, here's how you do shomen uchi, etc. The main difference is that in aikido we don't explain everything before moving on to the next level - instead, we explain every new technique as it comes along. This is the intoductory stage you describe, but it's not yet kata as I would define it.
Then comes the next step - and this is where, IMO, kata begins: integrating all these elements into a process that is more than the sum of it's parts.
In the car, this is where you start it up and begin using your new knowledge to drive the thing. And I can tell you, a driver who sits behind the wheel and tries to analyze everything as he goes along will be a crappy driver - much like the caterpillar who could no longer walk as soon as he started wondering which foot he had to move first. In a car, you'll now start driving around (at the end of my first two-hour driving lesson, I'd already spent one hour on the road, although at a leisurely pace and in only moderate traffic), see what you can and can't do (estimating distances, taking turns at the right speed, moving between obstacles...). In short, this is where you start applying your new knowledge to interact with your environment. Just like in aikido practice, kata are where you have to extend awareness of your actions beyond what you're doing, to also include your partner - and eventually, your whole environment. Without that, you're just mimicking things without doing anything that "works", and while that may be a form of practice, it doesn't fall under my definition (or many others', apparently) of "kata".
In short, what I'd call "kata" is the process where you integrate everything you've learned so far, and where you will practice this until you begin to grasp the principles that lie behind the form - eventually, ideally, entering a stage where you go beyond the formal restrictions and can act spontaneously, applying what you've learned without even having to consciously think about it - which would be jiyu-waza/randori in its highest, purest form.
I see all this as one long, organic process, and the boundaries between the three stages I described here are vague at best - as you gradually move away from one, you'll slowly move more into the next, except that you never really leave or enter one because they're not really separate (this is where the concept of "beginner's mind" becomes so much more important, I guess). I just wonder if you're not limiting yourself too much when you hold on to your definition of practicing kata as merely an "introduction stage".
Other analogy: I'm a graphic designer, and I've discovered the same similarities between aikido practice and free-hand drawing (=martial art & graphical art) - start by learning what your tools are and what you can do with them (=intro), then learn to look and analyze, and let your hand draw what your eyes see (=coordination, integration = form = kata), and eventually just draw what you see without hesitation, stop thinking about things like perspective or anatomy, or how to hold your piece of charcoal - and it'll work, because these things have become a natural part of the process and they'll happen naturally without you having to "control" them. The same principles apply to everything, really. Drawing from an analytical point of view and trying to focus on the many technical details will get you nowhere (trust me, I learned that the hard way), just begin without worrying about the result (or whether there should even be a result) and do it. If you fail, do it again, without holding anything back - eventually all the pieces will click into place.
I'd like to rant on, but it's getting late and I need sleep now. And anwyay, I think it's getting clear that we're just bickering over the meaning of a little four-letter word, not the process of aikido study itself ("any discussion, if continued long enough..."), and i've been talking way too much about aikido and doing far too little of it. Later, when we're both 8th dan, we'll laugh about this