The justification in the literature is that since all types of intelligence are correlated, just testing a relatively neutral one like progressive matrices is a

The justification in the literature is that since all types of intelligence are correlated, just testing a relatively neutral one like progressive matrices is a good choice, since it would generalize out to other types of intelligence. The flaw in this is that types of intelligence are correlated on average, they still vary within an individual, so IQ tests may say something about populations of people, but they are a poor assessment of an individual.