“We all know that anxiety has nothing to do with bitachon or lack thereof… The same way if someone is anxious, it doesn’t help for them to put more locks on their doors (it even hurts usually). Because anxiety is irrational.”
I understand your analogy to anxiety despite extra locks. However I disagree with your argument.
Yes if Bitochon was supposed to be simply knowledge in your mind then your analogy and your argument would be correct. The flaw in your argument is that Bitochon is supposed to be something you feel in the deepest levels of your heart, like a child who feels safe with his father.
Anxiety is an emotion, so if your Bitochon is a logical thing only then yes it won’t counter anxiety. However deeply felt Bitochon which goes deeper than the feelings of anxiety will counter the anxiety.
Obviously this isn’t easy, and for many people perhaps psychologists have other ways of countering anxiety which are easier to practically succeed with. However to state that proper Bitochon isn’t an antidote to anxiety, is wrong.
How do I know all the above? I’m not making it up. [Actually PBA’s argument seemed very strong to me until I did chazoro of the relevant piece of Mesilas Yeshorim, which helped me to realise the above. Yet again we see the danger of talking from the boich about hashkofo inyonim. Whenever one comes up with an idea like this it has to be tested very carefully by going through the relevant sections of the classical mussar seforim].
The Mesilas Yeshorim is in Perek 9. Well worth learning through properly.