Let's remember that Kote Gaeshi is literally a forearm turn. It is not easy to do the traditional supinating wristlock (kotegaeshi) when it is a closed fist. A traditional open hand shomen (tegatana) attack yes very possible. A tightly closed fist not easy to do kote gaeshi.
However, if you concentrate the forearm rather than supinating wristlock, kotegaeshi becomes easier to apply. Please note, make sure you throw uke from his back foot, otherwise he can turn around and punch you when he is doing ukemi.
Have a look at Osensei's photo in this post. Also look at the videos of masters doing kote gaeshi.
Notice that they lock the forearm and they put the forearm behind uke rather than concentrating on the wristlock.
A smooth kotegaeshi executed without pain is a superior type of kotegaeshi. Don't rely on pain with kotegaeshi, you will just get a stiff and reactive uke that will stop your technique.