An interesting topic, to be sure.
My first lesson barn made us tack up the horses before we rode, and untack and cool them out afterwords. At first I didn't like it- but boy oh boy am I glad for that. I'm sure I eventually would have learned how to do the mechanics of care, but their philosophy has stuck with me, and I really believe in a 'total package' lesson program, that includes horsemanship as you describe it.
I will admit that riding to me has always been my heart's calling. However, it just always seemed right that you spend at least as much time on the ground with the horse as you spend riding, and frequently more time. Riding is really the icing on the cake- everything else has to be there before a ride can occur.