This thread's got me thinking.
I hadn't carefully considered gokyo. I always accepted the Iwama explanation which is basically: the transition from atemi to controlling the wrist is quicker and the tanto can't be used to reverse the technique as easily. I was told that the grip differentiated gokyo from ikkyo. As far as the takedown is concerned, I don't think anyone here would argue that they are mechanically the same. I think too much is made of the reverse grip. Chris pointed out in an early post that there are ways to do nikyo that look very different, and that you can apply different pins to kote gaeshi and sankyo without it being called a separate technique.
I'm leaning toward what Ignatius eluded to earlier. Gokyo fundamentally is a different way to manipulate the arm/wrist/elbow. Ikkyo uses the elbow with its natural movement, nikyo over-rotates the radius with the hand directed back at the body (adduction), sankyo is an internal rotation of the forearm, yonkyo uses the ulnar or radial nerves, gokyo hyper-flexes the wrist -- palm towards elbow, and rokyo uses the elbow against its natural movement. This makes sense.
Although "kyo" only means lesson or teaching, the first six techniques of aikido are often viewed as pins. Many refer to them as osae waza. I think this can create some serious distortions about their most effective applications. Increasingly, I view these techniques as ways to cause someone to let go of you or something they are holding, or to quickly change their direction away from you. Not as means to take someone to the ground and fully immobilize them (I don't rule this possibility out). This is more consistent with aikido's relation to the sword and multiple opponents.