The approaches I have seen on these exercise have all been strictly external and focused on strengthening and loosening up muscle and joints. Now I believe that is part of what they were intended for, but I also think there is more to it that addresses internal development as well. However, without knowing what should be happening internally, that part of the exercise will be lost.
For several years I have trained in lineage of Nobuyoshi Tamura. He often did very extensive aiki taiso (about 40 minutes). Never explained anything. I have also practised under Suganuma Sensei, same story. How can you expect your students (some of which eventually become teachers) to understand? It is like to them these exercises are common knowledge (i.e. know what they are for), while for 'us' they are not and are basically left in the dark.
Sometimes I think this intentional...