I think it has been covered by a few folks earlier. First we have to define the purpose of step sparring, and I think due to it's origin, there are multiple purposes for step sparring. I do not personally feel that any of those purposes are
best trained in traditional step sparring.
It is my understanding that step sparring did not exist in its "traditional" sense in Karate until it's "modernization" in Japan. I have read that it was an attempt to make Karate more palatable to the masses by incorporating something familiar. Kendo and Judo had these step sparring exercises, which made sense in terms of beginning in A). a dueling distance rather than a more realistic "self-defense" distance and B). unbalancing your opponent multiple times prior to the throw.
This combined with a lack of breadth and depth of kata knowledge, it became an exercise of shadow boxing in a non-realistic situation.
A). the distance is wrong. The beginning attacker is often a couple of meters away! Generally, your attacker will be closer.
B). the attack is unrealistic. The likelihood of an attacker stepping with a reverse punch is not high in a self-defense situation.
C). the defense is unrealistic. Your "ready position", again distance, attack from a flawed position, how do you train an effective defensive strategy from a faulty premise?
D). Tendency towards overcompliance of the partner.
All of those detractors to being valid avenues of productive, realistic self-defense training has lead to focuses being placed on other aspects of step sparring. i.e. Timing, movement efficiency, technique, etc... I don't think any of these are bad, but I do feel they are better trained in other areas.
The premise of step sparring as I was traditionally taught echoes GM Weiss' explanation; effective, efficient defenses that deliver the
il kyuk; one strike-one "kill". My organization grades step sparring at each rank grading, so I do practice it in class settings in the manner it was taught to me. Efficient movements that allow me to deliver an altercation ending blow quickly.
So now that I've offered both my opinion on step sparring and how it was taught to me. I will offer a bit of how I teach the "choreography" and teaching strategies. I do my best to introduce a hand full of techniques from each of forms at each rank in the step sparring environment, as it helps with teaching the "entry" to the technique without the variables of live sparring. It helps to highlight the optimal positions/postures/steps. We also teach ways of demonstrating the more advanced kicks, although again, I'm not convinced of their merit to self-defense training per se as much as it is performative.
I have linked the one step and self-defense portion of my most recent promotion for video evidence of what I do when performing the activity/exercise.