One day I asked my Chang Taiji teacher, "What speed should I do my Taiji form?" He said, "It depends. If you just got off bed, your breathing is slow, your Taiji form will be slow. If you have just run 3 miles, your breathing is fast, your Taiji form will be fast. You let your breathing speed to dominate your Taiji form speed and not the other way around."
As far as I know, I have not heard any other MA system that use breathing speed to control the form training speed.
When you (general YOU) throw a punch at your opponent, your punch will be an exhale. You will never add an extra inhale in the middle of your punch. So, if you don't follow this Taiji guideline (1 move = 1 inhale, or 1 exhale), you are violating the basic combat principle.
I don’t know much about Taiji. I trained it for a decade or so and finally set it aside as something that probably isn’t the best match for me personally. This happened as my Tibetan crane was improving. So I comment from a Crane perspective, not Taiji perspective.
In crane, we do not worry about the breathing other than to say breathe deeply and naturally, and specifically do NOT match breathing to a technique, such as an exhale on a punch. Whether we are exhaling or inhaling on a punch does not matter. And the exhale or inhale will likely last much longer than a punch, so several techniques could happen during one exhale or inhale. Just breathe.
When you exhale sharply on a punch, you are trying to squeeze power out of your body, rather than letting it happen naturally. This becomes labor-intensive and results in the work and effort being done by the upper body, leading to exhaustion. You work harder than you need to. I realize most people do it this way with lots of effort which leads to lots of tension, (even when they believe they are not) and it seems to me that most styles teach people to punch in this way.
It does not need to be done in that way. When power comes from the ground, through the feet and legs, then you can relax the upper body and let the powerful legs do most of the work, while breathing naturally. Then a powerful punch becomes much more relaxed, much more effortless.
If you are squeezing out the power and exhaling on each punch, you get winded quickly. By not doing it that way, I could stand there and throw 100 full-power punches while carrying on a normal conversation because the work is being done with the legs and it becomes similar to carrying on a conversation while walking down the street. When you walk, you breathe naturally and you do not time your exhales with every step.
I do not believe it is possible to carry on a normal conversation while throwing 100 punches if you exhale on each punch. That kind of effort and breathing makes one too tired to keep talking.