involves a client and a therapist talking to one another. The therapist tries their best to see things from the client’s point of view, and offers something Rogers calls “unconditional positive regard” while they basically just rephrase whatever the client is saying back to them from their own perspective. It’s more complicated that what I’m describing, but the jist is that the therapist acts as a mirror for the client, and the client is then able to recognize themselves as maybe different than they thought they were.

Sounds like trening of mentalization.
Here is interesting document about theraphy: https://icpla.edu/wp-content/uploads/2018/10/Adolescent-MBT.pdf

I am interested in typology for self-therapy purpose in the first place. CT is another useful framework to look at psyche. But I am at beginner phase of learning CT yet (I am learning a lot of stuff beside that). I am happy that model 1 is almost finished. I prefer to grasp whole picture at the once.

one can know conclusively one’s own cognitive architecture and tendencies is pretty groundbreaking

It helps a lot. I like idea to surround my knowledge around model of functions. I always looked for base for my reflections and I think I found.

It’s really wild to think that we may both process information in totally different ways, but that we may share those patterns with others of the same type. I realize that this is the very foundation of the CT theory, but it has some very cool possibilities of it ever makes it to the stage where it can be used in commonplace therapies

Knowing cogitive processes can add nessesary details and can help to customize theraphy, speed up whole work.  I understand myself better now. It takes a months for my psychotherapist to find out things that I knew a lot faster from JCF theory.