Exhaling deeply helps relaxing the muscles and thus removing muscular tension. Getting a massage would have a similar relaxing effect, so I don't think this particular fact is very interesting.
More interesting is how breathing exercises can condition the suit, so that the suit can carry more of the load (besides the bones and a small amount of muscle). Basic idea behind these exercises is to adopt a posture that stretches the suit and then do deep abdominal breathing or reverse breathing. (Are you familiar with the concept of the 'suit'? The word has seen some use on this forum before, so I'm assuming you are.)
Of course, you can do the same thing during kokyu-ho to make as much use of the suit as possible to carry the load. Engaging the suit in this manner can be seen as a way of dispersing the tension as it makes your body better at bearing a load. Otoh, stretching the suit also results in a particular kind of tension and so does reverse breathing, although pressure might be a better word than tension when referring to the relation between the suit and breathing.
To be honest, I don't really focus on my breathing while doing kokyu-ho; there are more important things for me to focus on at this point. During solo practice I do actively work with my breathing and I have noticed there is some carry-over to partner work.
I can also imagine that you can do more complicated things with the breath, although I would be careful not to become too dependent on having to time your breathing with what you want to do. Don't know if that would be an issue.
I'm aware of the concept of the suit. Mike Sigman allowed me to join his Qjin list where this and many other concepts are quite thoroughly explored. I haven't been there for a while, though. There's a very deep level of information that can become overwhelming to someone who doesn't know a whole lot.
One of the nice things about the discussions about these things on aikiweb is that the information is fairly basic and a little easier to follow.
I haven't had direct exposure to anyone who has taught this specific concept directly, so I may grasp this concept differently from you or others who have had such experience.
One concept I have of how the body works in relation to this is that "lines of force" emanate from/via the tanden region referred to by Ignatius previously. This is why it's so important to isolate this "Thing" and actively develop it. I'm currently interested in the various approaches to pressurising (ie excercising) the tanden.
I know there are many approaches (RE the Abe quote above).
The ones that are particularly pertinent to this thread MAY be via breath and certain types of grabs in seiza.
So I am particularly interested in using Kokyu (breathing) to develop this at the moment. It sounds to me like you have other approaches to this.