I like to see kotegaeshi as an inward spiral, with the wrist twist at its center. The actual twisting of the wrist would be insufficient - and rather unpleasant - without the spiral leading into it.
I have started to explore the technique a bit on my website, with text and video clips - mainly because my uke Mathias Hultman does such a neat ukemi on it:
Beginners in aikido seem quickly to trust their kotegaeshi, but my first Japanese teacher Ichimura sensei used to warn us that it is really a very difficult technique. Thirty-something years later, I'm still working on it...