Probably, but one big issue is conservatives are traditionally loath to support single unwed mothers or even single fathers. For them it was a moral issue, other times it was bigotry.
If the government underwrote single mothers and fathers as much as we now provide in housing and food for some kinds of immigrants, in the past we would have seen a healthier population. They dug that hole. That is to Say Bernie of the 90s wouldn't have been much worse than what we find ourselves with today.
Don't reward single parents... reward families staying together and raising their kids how they want to, as decided by each individual family. There is a drastic statistical difference between those raised in family units vs single parent households... It's even significantly better to have grandparents (note the plural) raise a kid than a single parent.
It's not so much rewarding the unwed parents but supporting their children -it could have been community driven with grandparental involvement and so on, however, tat would likely be unpalatable for the small government minded --this could have been pushed off to other social institutions like churches --so long as one does not incentivize the wrong thing.
