It is not that intuition. The mainstream intuition is that a high heritability means that variations in the thing that you're measuring (height, SAT scores, infant mortality) is primarily affected by genetics and cannot be influenced by the environment. A better framing would say that high heritability means that variations in the thing that you're measuring are not well explained by existing variation in the environment. To reframe, then, what I was going for above, a high heritibility is an upper bound on how much you can expect to impr...
It can tell you something about existing interventions in a variable. In the US, for instance, we spend years of effort and upwards of hundreds of thousands of dollars on primary/secondary school education, and we know that we do a very poor job of making sure that different students have similar education experiences.
So, if SAT scores have low heritability in the US currently, then we would expect that we could figure out which education experiences tend to lead to higher SAT scores and try to do a better job of making sure everyone gets those kinds...
Oops. Accidentally dropped a paragraph about whether you could increase height/SAT scores across the board with the existing policy levers. In that case, a high heritability doesn't directly say that that's unlikely, but you would at least have to expect to increase your policy setting to the point where most people are getting more of the nutrition or education or whatever than is currently a few standard deviations above average, since otherwise if less than that much of your policy was having an effect, you would expect to already see it in ... (read more)