So much to say on this! Twin studies are useful, but very far from conclusive. And for a complex behavioural trait like IQ, not that helpful because a) IQ is likely an omnigenic trait; & b) the findings of 'genetic' effect in MZ twins could in fact be cultural transmission.
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It's a common angle you will get from, say, Turkheimer and generally people who approach these things from a philosophical angle instead of practical-empirical. Environmentality (1 - H²) is a kind of crude index of the malleability of a trait, sure.
You can make predictions of likely efficacy of interventions based on variance analysis. If it targets environmental variation already known to not affect the trait, of course, intervention won't work (e.g. parenting reading to enhance adult offspring intelligence).
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But if there's no or little variation in some environmental context and your intervention would produce a large increase here, then it could conceivable alter the trait of interest. Usual choice of example is PKU, which is caused by combination of genetic defect + specific diet.
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In that case, almost no variation in the diet for relevant property (all diets contained phenylalanine. Intervention produced a large chance in that environment for the relevant population, and thus was not excluded by general high heritability of intelligence.
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But if the intervention proposal is dietary advice for parents to alter BMI of kids, yeah, there's lots of variation in that already and it's not linked to actual BMI of kids (approx. no shared environment), so that intervention has very bleak prospects. Try something else first.
End of conversation
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