I really don't recall what the purpose was. I use it as an excercise in being able to isolate and control muscle groups that most people just don't think about.
Myself personally. And this applies to more than just aikido. I have asthma. When I start having difficulty breathing I start concentrating on breathing. This is one of the exercises I might do. It helps me get my breathing back under control. I have not used any meds for my asthma since I started concentrating on breathing. (I am not advocating that anyone stop using their meds at all) It also helps me to calm down and relax when I start getting anxious, tense and reactive which sometimes does happen during aikdo practice.
Try this exercise. Sit seiza and have someone push down with both hands from behind on your shoulders. Breathe in slowly through your nose, expanding your diaphragm downwards. Imagine your core is becoming denser and your body inflates from the center. When you exhale slowly from your mouth, allow your diaphragm to naturally rise upwards. Imagine your core is becoming lighter and you feel a firmness throughout your surface area. When you breathe in, the person pushing should feel a sense of pneumatic expansion and when you exhale, the person should feel a sense of being led to your center. Let me know how it goes.