fight, flight, freeze or fawn are I think by definition not cognitive choices, they are autonomous response of the nervous system. They take command and priority of cognitive control.
The only way to avoid happening, is to make sure the system threat isn't triggered when you dont' want to it. And this most certainly has both neurobiological explanations as been affected by previous traumatic events or training.
In see one part of training in MA, is the attain a level of perception of control, even in escalated situations. This is what will increase the treshold for triggering autonomic responses.
Edit: For me i see this as part of the mental conditioning. Ie getting used to taking hits, know how it feels etc, means you are no more control. For example know that, this will hurt, but I can take it, I will love, increases control, and knowing exactly what you have to deal with if you consider trading one attack for another. I learned alot here since I started. Exactly how much does this or that hurt? When is it fine to accept one, if i can trade it in for an opening for a counter that is more destructive? This kind of tactics is whan I like to think of. Trade a slap for a fist, trade a feet for a knee, trade a torso kick for a head kick.. all good trades. I think the idea that you can win without pain is somewhat of an illusion.