The example was public speaking. Many people get very anxious if they need to do that. But if they think about it rationally they realize there is no real danger there. That's how they know it is an irrational fear, and they can use the breathing technique to make it managable.
So maybe it's more about if you know you should not or can not run away from a fearful sitution you should take a deep breath. Whereas if you are on a dark street alone and a group of hooligans look like they might attack you then feel fear and instead of breathing deep, you should run.
You say fear is good, presumably because it stops you from doing things you don't know are dangerous.
But then you say you can do a technique to defeat fear when you know the fear is irrational.
But your argument starts from the premise that you don't know a situation is dangerous or not without the fear so how would you know it's irrational?
In my experience it's the opposite, most fear is not useful.