Nitpick (since I don't dispute your main point): Parents aren't the sole source of influence in a person's formative years. Kindergarten, neighborhood, peer group, school are just as if not more influential. In fact, some promising ways to inject higher quality human capital than some families are able to provide on their own rely on those other channels.
What do you think best predict what kind of neighborhood someone grows up in, what kind of kindergarten that can be afforded, peers someone has a chance get to know and what schools they will attend?
The chain of causality from parent's success (or lack thereof) to children's success doesn't only go via the parents direct influence on the children, but probably more through the environment they have the means and foresight to provide.
