There are plenty of psychologists who will admit that these tests are unreliable.
Think about it. What qualification does any psycho have to even imagine what sort of person should be driving the jet?
In reverse, do psychos think pilots are qualified to say who is a good psychologist.
It sounds like chalk and cheese to me.
We have a tried and tested system of country CAA approved check pilots whom you have to satisfy before you can take a seat in the professional cockpit. The system only breaks down when the chain of command allows the wrong people to be the trainers/checkers.
Don't allow psychologists to select pilots until pilots are allowed to select psychologists.