Of course the thing about systems of rules with people is that they react to incentives in inconvenient ways. At best they would save less to pass on if nobody they cared about would receive any of it.

Really if we valued equality of opportunity at all cost we would either collectivize or randomize children but needless to say that would be incredibly unpopular and not lead to good outcomes given aspects of mammalian child-raising and bonds - we already know from our experience with orphanages that calling the results sub-optimal is an understatement.