You seem to imply men and women are the same and should be treated the same in the context of sex. Which is not the case. Just as men are drafted for war, because they're men, women are overlooked because they're women.
Same in hostage situations or disasters. Women and children are given priority. Is that fair? no but that's because every thing serves a purpose for the most part. Societies function properly due to the norms set.
Sex is a tool, an extremely powerful one. What does sex directly create? babies.
No one has the time to help someone with their lawns unless paid. Taking care of another man's baby because he pumped and dumped is not something 99.9% of healthy virile men are willing to do.
So how do you stop the epidemic of unwed single mothers with children from depending on welfare and the state?
the most powerful tool would be the people themselves. Make the culture that mitigates the creation of single mothers which includes "slut shaming" etc.
Men don't get pregnant or receive benefits when financially dependent which is what we call a hobo. So everyone has problems.