There are two kaeshi waza in shodokan aikido: The first,
the ura-waza kaeshi waza which is a set of ten fixed counters. The origins of the kata are unclear to me although I can see why each techniques makes perfect sense to use as a counter.
The second is the Tanto kaeshi waza which is a set of fourteen (dropped to ten in gradings1) counters while having a tanto in tori's arms. The kata was developed by Nariyama as a way to promote counters in randori by teaching tanto that they can either stop and re-direct the attack or blend and accelerate it. It is a set of ideas based on those principles. As part of making Aikido ones own, one is expected to learn principles from it and apply those to whatever works for one.
Clearly, the ura-waza exhibit the same stop & re-direct or blend & accelerate movement. I am unsure if it was a first atempt at teaching those principles or something else I have not groked. Thus my earlier question.
As a special case, Kote gaeshi can be countered by itself, ushiro ate, and gedan ate: we see this in both kaeshi-waza. Which one is best? Clearly, the one you can do under pressure. So, most (if not all) of the techniques of the randori kata could be countered by any of the other seventeen ones. Although some combinations might be a little contrived and would probably not work under duress.
Note that during randori, tanto can only retaliate with the five atemi-waza so training those makes more sense than working out all possible combinations. Also, a counter is tricky to execute so a simple technique will be easier to get right than a harder one.
1: The drop was because you do them as uke first, then as tori. This means twenty four techniques on top of the seventeen tanto randori and sixteen (or more) of the goshin… It all takes too long. Thus, a simplified version is used for gradings.