Why does it seem like we can improve our bench press, minutes-per-mile, or alcohol tolerance much more than we can increase our IQ? Can a person with a 100 IQ get a 120 score after training? 130? Seems quite believable to me.
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Suppose you could? So what? People aren't doing it because there's no reason to do it. If nobody worked out your squat would be a good measure of your genetic strength. Iq is like that even if it's possible to study for it.
I suspect that many people engage in activities whose byproduct is a higher IQ score. Some even do IQ tests for fun. I did that as a teen. If IQ is used to judge, label, sort people, then that's an issue, one, I think, that is corrected by markets, but still worth publicizing.