Yeah, that's good. Besides Buddha's Warrior Attendant Pounds Mortar, there are equivalent practices in a number of other arts. There are partial practices in a number of arts (e.g. the fumikomi in Kendo, the step/stomp in Xingyi, etc.) that are undoubtedly related from long ago to the same practice. That's why it would be a little silly to tell, say, a Chen-stylist that "I've never seen you practice Shiko".
I can think of two ways to look at this:
1) What is the end result of doing these specific exercises a lot? You get better at the specific exercises. They each have a set of external demands placed upon the person doing them (i.e. foot here, arm there, etc. etc.) that are different between all of them or else they would look exactly the same. So rather than say they are all birds, call a duck a duck, a turkey a turkey, and an ostrich an ostrich. These external demands are there to teach something about how one is to do the exercise in question. Now, it may be possible to generalize principles from the form of the exercise about other movements, but the result of the exercise is bound up with the form, because the form defines the utility of the exercise.
2) If, following these external demands, it is still possible to do the exercises "wrong" or that it is still possible to do all these exercises the same "way" regardless, then there are, in fact, demands not intrinsic to the exercise, and you could go so far as to say the exercise in question is actually useless and pointless for teaching them. The necessary demands of the exercise are not bound up in the form of the exercise itself. Why do an exercise to learn something if it doesn't specifically teach it? You could just as well rub your belly and pat your head over and over and practice whatever underlying principle there is and it would be equally effective as doing Shiko or Buddha's Warrior Attendant Pounds Mortar or xingyiquan or....
Which of those two ways of looking at it is it? I dunno. I got my own vague answers, but I would rather pose these as questions.