Intelligence testing came from the field of psychology, but now mostly gets used by employers, the military, schools. AI researchers make claims about intelligence of their products so they can sell AI products.
And even if GPTthings are or become minds, you run against the next problem: psychologists study human minds. If fields analogous to psychology become useful for AI, they will have to be specialist fields because they certainly wouldn't be human and so would be outside the field of psychologist expertise. Much like psychologists don't study animal minds.
Yes and no. Binet and his colleagues who created the first intelligence tests were psychologists. But in the 120+ years that have passed since, psychologists have determined that intelligence testing is full of problems, and have mostly abandoned them in favor of targeted assessments.
Because GPT is an algorithm which implements a predictive statistical model and does not "think".