Is exhalation strongly associated with striking, or is this just a perception?
If it is the default for striking, what physiological principles make it optimal during strikes?
If this is a general principle, does it also apply to throwing, and, if so, is the physiological benefit derived differently than in striking?
The exhalation is not linked to any particular sports, but a rather profane mechanism: Tensioning of the abdominal muscles reduces the volume of your lower abdomen and thus pushes your diaphragm upwards, which in turn reduces the volume of your lungs so that the air has to go somewhere, voluntarily or not. Any kind of lifting, crunching, or torsion movement will involve the muscle belt between hips and ribs which is the actor in said mechanism. So this definitely holds for throws as well.
If you have breathed in and close your windpipe consciously when making these movements - especially against resistance as opposed to fluid movements - you will notice a strong pressure in your throat and abdomen because of compressed air excerting pressure from within your lungs, effectively resisting the compression from the outside. This pressure can become high enough to make your alveoli pop and hurt your lungs. Before that happens, your body automatically loosens muscle tension to protect your lungs from injury. This involuntary relaxation, in turn, will inadvertently lessen the power of your move.
This is why we train relaxation and breath flow in martial arts: To train not to have so much tension that we close our windpipe, ie. "hold our breath", when we actually should not. Breathing in and/or stopping the free flow of air is a natural mechanism for "bracing" for some kind of force, but it is detrimental to the outcome in all martial arts situations, may it be striking, throwing, falling, or being hit. A secondary effect is that if you consciously breathe out forcefully, you engage exactly the muscles you need for the proper transfer of force through a stiffened frame.
Therefore, regardless of the level of the practitioner or the sport, if you do not exhale (or have exhaled) in powerful movements, you make your body work against itself, no matter how you describe the mechanism (ie. in terms of physiology and physics, or qi, or whatever). The reason why doing a pronounced exhalation at this moment exactly is optimal is that you support the tensioning needed and lose less time with air inhaled, ie. you can generate more energy over time. Especially the latter is a very important factor in fights, which extend over time, as opposed to one-off movements.
In other words: The more power you generate through your abdomen and the more powerful and longer the engagement is, the more important it is to exhale consciously. In any case, you will want the air in your lungs to be able to get out when you need tension in your abdomen. Since powerful striking and throwing which does not rely on fluent full-body movement but acceleration from a stance instead generates a lot of its power through the abdomen, you will want to exhale doing it. This will not be similarly pronounced when generating force through bigger and/or more fluent movements, but for the moment of contact or final acceleration, it should and - if executed properly and with great power - still will be there.
This is similar to the effect when forcefully exhaling during weightlifting - the forceful exhalation (different to the Valsalva manoeuvre, which is also employed in some situations) creates not only a rigidity in the abdomen which allows for more efficient force transfer, but also increases muscle tension globally.
This is useful for the martial arts because exhaling forcefully at point of impact will improve our force transfer and also tighten the muscle in our striking limb to mitigate injury risk (for example through having a more stable wrist).
It should apply to throwing equally well (as well as attempting to prevent being thrown) as it also applies to throwing events in strength sports (shot, weight over bar, etc.). This relates to non-throwing takedowns too.
I think part of the association comes from kata like sanchin and hangetsu, as well as the specific breathing associated with many Chinese martial arts - I've not seen as much of an emphasis on it in western boxing, but that may be just me.
My anecdotal perception is also that people will naturally fall into this pattern without coaching as breathing out while exerting is a natural biological response (watch someone lift a sofa and they'll do the same).
I would wager the breathing will remain in more advanced fighters, but become less pronounced as they develop the ability to time their breathing better with their strikes, and loosen up only needing to tense at point of impact (beginners tend to be tense all the way through a technique), but I have no evidence for this position.
Hopefully that helps!
I can state that it is not a universal principle in martial arts. In both Doce Pares Escrima and Capoeira, I was specifically told not to tie my breaths to strikes, but rather to focus on breathing evenly and naturally during the movement. This is basically because, in both styles, you're expected to be blending strikes into fluid sequences rather than a set of distinct strikes. Completing one strike is tied to starting another.
As to why forceful exhalation is strongly associated with strike in martial arts, it's likely for a lot of the same reasons covered in Why do martial artists "shout" in the execution of a technique?, namely the physiological benefits of focus, coordination, and possibly distracting the opponent by cueing them into an attack coming.
And, again from my experiences in Escrima and Capoeira, you may still get the occasional shout for emphasis or to startle an opponent, the same way that a tennis player will yell or grunt on a particularly hard volley, but is unlikely to do it on routine swats.
