We don't train with the idea of being prepared for the other hand.
What we do watch for is whether you have ukes center/balance all the way through the technique.
Perhaps its just a difference in how you visualize it. Being worried about the other hand might make you train so your partner is off balance and can't follow up their attack with their other hand or foot, etc.
Focusing on having our partners balance also helps us avoid clinches and any other counter movement they might try too.
I also might add I have been surprised to find some things can be done even when uke has poor balance. Some kicks can be fired off even when a good kicker is wobbly.
The impact might be less though if not delivered from a good base and you could perhaps survive a hit or two like that.
There is a sub context to the thread re: kotegaeshi. Our Shihan teaches us Kotegaeshi and Kotegaeshi Nage. From my understanding the basic Kotegaeshi won't cause uke to go flying over a distance rather its the rolling of the hand/forearm pretty much so uke falls in front of you. He might go head over heels or not depending on the force. If you want some distance you then apply a nage version of kotegaeshi and that is when uke might land feet away from you. The body motion for nage feels different and is connected to the handwork.
When I first started I thought Kotegaeshi was just Kotegaeshi. It wan't until later that I found there was a difference.