I'd love to have a class that focused on nothing but kaeshi-waza and henka-waza! All techniques have a counter move - - the "cost" of that counter may result in the uke taking damage (i.e., actual injuries); if the cost of a counter move is low or null, I'd consider that to be a good point for a kaeshi-waza response....
We should strive to practice "active resistance"as uke: there is not just one attack per encounter - uke is striving to take any advantage s/he can (reasonably) get during a technique, to show Nage where the "holes" are in their technique. That's a standard operating procedure at our dojo.
Akira Tohei Shihan often said, "Touch - same as hit; Hit - same as kill." That is to say, if uke can touch or hit the nage during a technique (with their free hand/foot/head/etc.), it's an indication that the technique has some flaws in it's execution.
We also practice kaeshi-waza and henka-waza in our advanced Aikido classes, and "on our own" during free-practice periods. It's this principal of "active resistance" taken to a higher level. In this kind of activity, there is no uke or nage -- just like-minded aikidoka at play. (The "touch/hit" rule applies throughout the encounter.)
It's a great way of training for good technique, but requires both partners to be highly aware of when they are in a position of "significant disadvantage" that means that they cannot reverse the technique without self-induced injuries; at this point, they tap-out. They must both recognize the damage-danger-point, and disengage. "Staying soft" allows them to communicate through their bodies as to what the current status of the encounter may be.
Think of kittens at play -- the claws are out, but they shouldn't be penetrating too deeply (or someone isn't playing fair).
Note: you cannot train a beginner to do this -- they don't have the vocabulary yet. Advanced students seem to pick up on the "touch/hit" form of communications, and at some point, add kaeshi-waza and henka-waza into the mix when the spirit is right.
So, Chris, if you're not there yet, you're obviously getting closer to that point... you just need to find a like-minded "sparring" partner.