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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.