Providing such benefits to those below poverty level doesn’t make sense to me. People are that level of economic value need to improve their situation before taking on the burden of children. Taxpayers should not be subsidizing the poorest to have large families they can’t take care of. The opposite should be happening - we should subsidize households with demonstrated capability to be successful (which in our society does mean economically) to have more children.

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