Subsidizing the broken families (and those who are on welfare are almost never married) does not help society.
Ending the subsidies for more fatherless children will incentivize proper family formation, even if it simply means curtailing the growth of a socially broken underclass so that married women have a lower financial burden and can afford more children.
It's like thinking marriage is helped by contraception. I was once witless enough to believe that: but that was 40+ years ago when I was a teenager. One of the main things contraception has done is destroy the marriage culture.
In 1965, the nonmarital birth rate in our own black underclass was something like 1:4, and Daniel Patrick Moynihan was vilified for saying it was a "crisis" and the "disintegration" of the black family.
Moynihan, of course, was right.
Now the nonmarital childbearing rate is 1:4 for Whites --- and for Hispanic 2:3, and for Black 3:4.
What's destroying family-formation is not lack of contraception.