Things like MBTI and enneagram and such are frameworks to talk about cognitive functions and all that. Holding them to the same standards as physics is a bit silly.
They don't talk about cognitive functions. Those would be things like vision and memory. And I'm not holding them to the same standards, but that doesn't mean that any old balony is fine. People attach a certain value to psychological tests, and they should realize that the whole thing is rather arbitrary.
You're right that they don't talk about cognitive functions. That's only when looking at these personality traits as a categorization of the outputs, which would feel like arbitrary curve fitting.
To be more nuanced, the underlying basis for MBTI on cognitive functions is about describing the input processing of various personality types, which isn't obvious (and completely obfuscated) if one is reading descriptions on a site like 16personalities.com.
It's a subtle but nuanced difference, but provides an avenue for therapists to understand how inputs in a client's life may affect them and their responses to situations. This is a more valid dive into the input-processing aspects of MBTI: https://www.typeinmind.com/type-theory
If you read the type descriptions on the typeinmind.com website, you'll see that the approach is very different. It may seem arbitrary and foo foo, but I'd challenge you to look deeper before completely writing it off as bologna.
