Hi all, just from my limited point of view (and few years of karate) kotegaeshi is an absolute smorgasbord of nasty opportunity when it comes to atemi. Everything from head butts, hook punches, empi strikes, and ankle sweeps. I my humble opinion freezing up hard and zeroing in focus on keeping your wrist and arm tight is almost suicidal from Ukes perspective.
Ps I have been on the wrong end of just such atemi by mistake. I've learned to move quickly
From my understanding the technique is predicated on uke doing just this as the intention of Kote Gaeshi is to break their wrist rather than throw them.