I suspect the freeze response is rooted in the same reason that many animals freeze in the face of a predator. It's an attempt to be overlooked. Many animals and I think especially predators, can detect motion better than they can process a still image. Of these three methods, none is the best in all situations.
The biggest problem with all three is that it's hard to consciously choose the best of these three reactions for any given threat, since they are triggered by the fastest, most primitive part of our brain. And even after our initial reaction, it's still difficult for our rational brain to overcome that initial response assuming it's not the best response, because we don't tend to think as clearly under high stress conditions.
In a genuinely stressful situation I believe it is as you say - we're not likely to be able to control ourselves and choose reactions. But in our lives there are lots of "repeated stressful situations", these are situations that we face from time to time, maybe daily, situations of similar kind (like performance in front of a big audience, necessity to get acquainted with strangers or climb to a great hight, etc). In these cases I believe we can choose our response through time by making this situation from stressful to an ordinary and familiar one. I believe this could be achieved through practice and continuous deliberate putting oneself in such situations, making the fear go away and learning which reaction brings us more benefit.
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Yes, I agree. This is one of the reason I think "veterans" are valued in combat much more than soldiers who haven't been in combat before.
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