Not a hill I'm going to die on, but the SAT has many attributes IQ-ists insist IQ tests are insulated from: it's straightforwardly trainable, culturally loaded, samples only math, processing speed, and verbal reasoning, and tracks prior educational experience as much as it does aptitude.

Draw-a-Person basically isn't an IQ test at all, so I don't see how that comparison clears anything up.

> Not a hill I'm going to die on, but the SAT has many attributes IQ-ists insist IQ tests are insulated from

This is false. In particular:

> it's straightforwardly trainable

No, it isn't. There is an extensive literature on SAT prep, finding that it's worth a couple of points on the test. It is widely described as being trainable, but the opposite was always a design goal, and historically that goal was achieved very well.

You might note that the Raven's matrices are infamous for huge training effects; that test relies on the testee having never seen it before. The SAT doesn't.

> culturally loaded

This claim is true, but nobody claims that IQ tests are insulated from being culturally loaded. The purpose of Raven's is to be a culture-free test. Wechsler makes no such pretense.

> samples only math, processing speed, and verbal reasoning

I'm not sure what you're saying here.

> and tracks prior educational experience as much as it does aptitude.

And this one is false. The point of the SAT is to test only low-level material so that you can be confident the entire test-taking population has been exposed to the material. Aptitude has a very large influence on SAT score; prior education has a negligible influence.

(Prior education will have a larger influence if the population you're investigating includes a lot of people with no education, the kind of people who left school after or before kindergarten. But that scenario isn't relevant to... pretty much any question about the SAT.)

> Draw-a-Person basically isn't an IQ test at all, so I don't see how that comparison clears anything up.

It is an IQ test by the standard you defined: it holds itself out as being "an IQ test", and it is used by researchers to study the intelligence of testees. Did you want to use a different definition?