Re: The point of aikido osae
Primarily, this context the martial education to which I am referring is either the knowledge of the henko waza that would counter my escape movement if the pin was improperly employed or the proper response to comply under the correct application of the pin. Think of a typical judo setup for a 2 or 3-technique series... I may counter the first move but likely that would simply create a better scenario in which to employ the second or third technique. Of a second reference, the context to which I am referring is the individual knowledge of what is the proper move I should make to escape a pin. So in answer to your question, yes, part of the martial education would be the personal knowledge of how to properly escape a pin.
In short, I usually address three responses to a pin: escape before the pin is applied (kaishi waza), resistance to an improper pin and compliance to a proper pin. I think many aikido FUBAR our responses because we cannot discern the proper scenario in which we find ourselves. We resist correct pins, comply with incorrect pins, and often don't know when the proper timing is to escape a pin.
I think many aikido people do not employ aikido pins severely in training. I am not talking force, I am talking about applying the pin at the right time and using the proper mechanics in a mental state that dictates the need for the pin to work. One time, one technique. That is to say that we often leave openings in our pinning techniques that may be exposed. Sometimes we train with sympathy for our partner that causes us to apply the pin a little less severe than is proper. Maybe my partner is sore, or hurt. Maybe I don't want reciprocal treatment. Maybe I don't know the person. Trouble is, that lapse leaves an opening that my partner may choose to use against me (in this context, escape or resist a pin). Graham touched on the second part, maintaining the effect of the pin after its application.
Now, for both responses I will clarify that I do not necessarily think it is bad to omit the severe application of kansetsu waza or osae waza. Nobody likes to have a successful nikyo applied countless times during class... enough times to understand if nage is successfully applying the technique is fine, but then concede that point and move on. However, I believe it can be hard to differentiate when a pin is correctly applied when uke does not posses the knowledge to make that assessment.
As a tangental point that I make about the severity in which we train and apply pins, consider the response as uke. Why would you resist a pin if you knew that pin could cause you physical harm? Consider that it only takes one technique, one time, to destroy your shoulder or your wrist.
Aikido is subtle. Sometimes too subtle. Osae waza is supposed to be a period at the end of a sentence, but on the mat its often one of the most contentious points of a technique. We fight it because we assume nage will not hurt us. Nage will let go, or ease up, or concede the contention...
I hope that helps clarify my post.