Women are inherently disadvantaged on a free market. Because they need to take breaks during pregnancies and the time after, women need more security and support. They also feel more connected and responsible for the newborn than men (who seem to "run away" more often than women) and thus have to bear more risk. Hence they are more "social" and are thus drawn to models of society many here would call "socialist".
The insensitivity of many libertarians and ancaps for this set of problems is one aspect that scares many "normal" folks (and leftists) away. I don't like the "big state" solution either, but the "free market" fails to resolve this. Also, women might complain that raising children is hard work, and an undoubtedly necessary service for society, but it is unrewarded by a market because what they do is taken for granted and the market cannot really provide a way to compensate them.
So until there is a satisfying solution for this, I predict we won't have libertarian/ancap "utopia".
The solution to this problem was invented thousands of years ago at the dawn of human civilization: marriage. The real 'till death do us part' kind, not the current completely unenforced version. Marriage is simply a voluntarily entered contract that solves exactly this problem. And a libertarian/ancap 'utopia' would have no problem enforcing any custom marriage contract.
What happened is that the left decided that instead of a private solution to this they would destroy marriage to force a public solution, hence the big government nanny state.
I responded something to this effect earlier and was labelled patriarchal and a right winger. Family as a contract is perfectly ancap in my view, and proven to work for thousands of years.