"The parents kept the money they earned, and (quite rationally) chose to spend it on giving the children an economic advantage (that the children, more often than not, could not have earned for themselves.)"

So the children, who could not have earned that money themselves, should get it anyway? Why are they particularly special -- why not redistribute money to other people who have trouble earning their way? Why does the fact that you are someone's descendant someone exempt you from having to earn your way just like everyone else?