Let's be a little cautious about the correlation between socio-economic status and innate smarts. There are powerful situational factors that can supress innate talent, and that persist from generation to generation.
Growing up poor, with no books in the home, parents who are gone all the time because they work two jobs each, belonging to a racial minority that is expected by teachers to underperform, and maybe even having been exposed to drugs in utero, not to mention the damaging effects of chronic stress on the brain, can all result in an adult who's brain isn't wired to perform as well as it could have under different developmental conditions. And guess what's going to happen to that person's children?
Yes, there is surely some effect of smarts on upward and downward mobility, but overall, mobility between SES levels is really pretty limited. (Equally true at the other end, by the way. Spectacularly stupid people who are born into upper class families don't tend to be downwardly mobile.)
Oh, I'm aware it's very, very un-PC to suggest it. But if you look at all the studies out there is becomes apparent that while there are folks who are "left behind" due to circumstance, by and large you cannot for account this gap. It's not due to early access to pre-school, it's not due to race, it's not due to time spent reading with small children, or other 'early literacy' activities. All of those things have been show to have very limited impact on a child's education.
IMO, we need to get away from all this political correctness. Political correctness is how we ended up with this silly idea that "every child is gifted in his/her own special way" and that every child can/should attend college! It's just ignoring basic human ability.
ETA: I disagree with your comment that "Spectacularly stupid people who are born into upper class families don't tend to be downwardly mobile." Of course they do. It's apparent when those idiot people have children. And when those kids have children. There are countless instances of stupid people squandering their inheritance and leaving their families broke.
