In those days we were taught to apply kotegaeshi without turning the wrist to the outside...which requires that the uke take a hard fall over the arm.....rather hand was wrapped into the wrist on the thumb side and slightly to the outside....and a drop and down. I have gone back to this as it is to me much more effective and causes not direct injury to the uke while getting them on the mat. You destabilize them, drop (slight) and imbalance...they are on the mat without an opportunity to recover.....the connection is through the wrist..elbow..shoulder and center.
We also apply kotegaeshi this way. The 'over the top' version is more spectacular for those watching, but in my view, I agree not as effective. It is possible for uke to escape the hard fall version, if they can keep up with the technique and 'follow' any undue force being applied, this can be reversed into a nice kokyunage.
From the point of view of the impact the different versions have on uke, the Tohei method is more respectful of uke's body. I question the need for multiple high breakfalls in aikido, there is a greater chance of injury, doing it this way, paricularly with inexperienced uke's.
If one was ever required to apply kotekaeshi in a real world scenario, an attacker is unlikely to have practiced ukemi, so all sorts of problems could arise.