Cutting off benefits won't slow the increase in the size of the herd. Cutting off something else might, and might be an incentive for the baby daddies.
For some girls, having a baby is their plan for the future. Take away that option, put the cost of their actions back on them and their parents, and all of a sudden having a baby at 16 is an act of financial stupidity in their eyes. Marriage might even come back in style.