If women were (legally allowed and required ) to be paid upfront for delivering and raising children, the market would sort things out. We would probably get some professional mothers who would have 6-12 children.
Who pays men for their role in raising children? Some men are primary parents, and increasingly so.
theoretically some women could pay some quality fathers for coparenting , but it would be rare.
It sounds like your idea is that women get paid to have the joys of being a parent, while men pay to get nothing in return.
If the woman and children do live with the man then essentially you are recreating the idea of a male provider married to a housewife, except more transactional and unequal.
The current situation artificially limits supply of mothers because it requires relative exclusivity of the father. It’s like nimby people not wanting apartments in their cities to limit supply. Except imagine if nimby’s were able to ban apartments all over the world. That’s the situation with motherhood. It’s single family zoning world wide…
Of course it sounds dystopian and is not about to happen anytime soon. Because cartel’s don’t give up policies that limit supply so easily…