That might sound attractive at first[1], but when we consider that there isn't a practical way to stop those poor people from having children anyway, what such a policy amounts to is that we punish such kids[2] for their parents' "sins" -- which is a great way to breed a generation of sociopathic miscreants bent on destroying your society.

[1] (if you can avoid thinking of the class-based eugenics that such a policy would amount to, if it were actually obeyed)

[2] punish by impoverishing them further, or by making it more likely they'll be neglected by those parents that you already suspect aren't responsible