How does your plan work considering kids have other needs besides food and diapers. Children need a home to live in which requires the payment for that plus the light bill, water bill, and gas bill. The mother needs a method of transportation so she can work and transport the kids. That requires car insurance at minimum. The home the kids live in needs maintenance if its not rented, that costs money. Child support is not just for food and diapers, it is so the child can maintain a certain standard of living. It is not solely on the mother to provide that.
This is why I don't believe in premarital sex, and if women were smart instead of falling for this false "empowerment" they wouldn't believe in it either. Sex comes with responsibility. If you don't want to be responsible then keep it in your pants.