Without welfare, the mother would likely give he children up for adoption by responsible people that can afford them. At least she would have that choice, and the choice to raise the children in poverty, thus causing them to suffer, would still be hers.
Judging by the responses to my "boilerplate," inluding yours which consisted of a run of the mill ad hominem attempt to shut down the conversation by white knighting, and others which were non-arguments and sarcastic these are not arguments that people have considered.