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It feels silly to frame it like that. You could consider a general education as practice for an IQ test.
The way I see it, IQ is a proxy for this concept of generalized intelligence with the test also measuring more specific measures of intelligence like working memory and visual processing. It's certainly fine, even good, to practice the underlying mechanisms of intelligence, such as learning memorization techniques and practicing to improve your working memory and thus become more intelligent. It's not good for the validity of the test to practice the specific questions and sections they put on the test to artificially inflate your score while leaving your underlying intelligence unchanged. Veritasium did the latter, not the former in his video.
But if you get more generally intelligent from practicing... Then what? Because education makes you score higher. Do you believe it is 100% genetics?
To some extent you probably get more generally intelligent from practicing IQ tests in the same way you might get more generally intelligent from stretching your mind in any way. However, the increase in IQ score you achieve after practicing for the IQ test is (just guesstimating because there's obviously no studies on this) >90% due to learning the patterns of IQ tests and <10% due to increased general intelligence as a result of studying.
To answer as to why IQ is helpful, it's useful for making conclusions about how different factors influence intelligence. It's more difficult to prevent lead from poisoning people's brains when you can't conclusively say how much it's poisoning. Supposing all the people with low IQ scores due to lead poisoning practiced for the test to make themselves feel better with a higher score, their studying would muddy the stats and make for weaker arguments on the side of those wishing to ban excessive lead. IQ is also relevant to certain diagnoses, such as for the diagnosis of ADHD where a deficiency in working memory and processing speed but not elsewhere supports a diagnosis.
In terms of whether IQ / intelligence is 100% genetic, obviously not, I don't think I said anything that could even suggest that. I'm not an expert so I'd appeal to this link for specific answers. Just skimming it seems to suggest anywhere from 50% to 80% heritability of IQ, although heritability as a concept is kinda unintuitive and hard to apply to everyday things.