Isnt it obviously true? If you don't breed you don't pass on your non breeding genes, if you do breed....
Living organisms are literally breeding machines, that's all they really do. Natural selection favours those who do it better.
And, going one further, in the past people had children as a matter of rote. Now, it has to be a deliberate, overcoming the obstacle of modernity, in a sense. In the same way smallpox had a habit of reducing the population's potential, so too (by a different mechanism) does education, birth control, abortion, etc. A subset of the population will effectively become immune to those things.
When they refer to education reducing potential, they mean higher education levels generally correspond with a lower birth rate, for a variety of reasons. So smart parents having smart children does seem to fit with that.
Or am I misunderstanding what you're getting at?
Hope that helps to clarify.
Both fertility and intelligence are not as simple as the color of someones eyes. Lots of genes play a role, so the combination of two favorable gene-sets does not necessarily lead to a still favorable gene-set. Therefore, there always seems to be a "regression toward the mean", so don't worry, one or two generations cancel out all "preexisting conditions". Therefore, in every practical sense, both the heritability of intelligence as well as the heritability of fertility are negligible compared to other factors.
Of course children of more intelligent parents tend to get a better education, for example, i.e. those children can develop more of their potential, but here we're back to environmental parameters. But hey, this is good news, because it also works the other way around - dumb parents can have smart kids! So even if dumb people breed like rabbits, we just gotta make sure schools are properly funded to educate those children properly so they can develop their potential!
Anyway, I often hear that claim of 50-80% but I can never find the publications backing up that claim. Can you list some, please?