Are you suggesting that children in poorer families are born less smart than children from wealthier families?
Unless, of course, intelligence is "bad" for the wealthy and "good" for the poor, but I doubt that's the case...
But intelligence without wealth can easily be beaten by average intelligence plus wealth and status. E.g. Trump
'Inheritance' doesn't have to mean just what was passed down at death - it must also include all the additional resources available during development to have any meaning.
But if you are saying that education makes little difference to lifetime earnings, you're going to have to back that up with a reference because it's an extraordinary claim.
You seem to be suggesting some sort of natural selection process, whereas it's also legitimate to posit that status contributes to higher IQ (or g, if you prefer) in the form of:
- fewer chemical contaminants in utero and in early life (i.e. living in a less chemically polluted environment)
- access to better nutrition
- access to better medical care
- less stress in utero and in early life
- less exposure to disease
- less exposure to psycho-physiological toxicity (e.g.: poor sleep quality due to a noisy environment)
The list goes on.
tl;dr: you're assuming causation from correlation.