That shifts the burden of looking after the children onto the state, since society tends not to accept starving children or mothers raising kids in grinding poverty after their deadbeat dads abandon them, whatever your own sympathies.

I agree that visitation and the presumption of kids living with their mother is an issue. Older kids often do have the choice to decide to live with their fathers - if they do so permanently, the mother must pay child support. The fact that men can’t decide to terminate a pregnancy is a product of biological reality. Men shouldn’t stick their dick in crazy, or better yet, shouldn’t be promiscuous at all (and at least should use protection), because that’s negative outcome for society.

Men who fuck the kind of women that leave them and take the kids and demand child support, and who do so without the use of easy and cheap contraception that is effective in 99%++ of cases, are idiots. They shouldn’t have our sympathy. Promiscuity is degenerate. You lie in it, you pay the price.