Jennifer Roback Morse, a researcher at the Hoover Institution, argues in a fine essay in The Meaning of Marriage that a libertarian society would not, in fact, want easy divorce. Marriage creates obligations which, if badly managed, create costs for society. Kids create obligations which, if badly managed, create enormous costs for society. Married people just handle both kinds of obligations, absorbing most of those costs and not externalizing them on society.
If free individuals never interacted with one another, then a libertarian state might be able to stay out of marriage and childrearing. Of course, no interaction would mean no kids, and soon enough no society. However, people do naturally couple and make kids. Marriage means they handle it, and the state doesn't have to. Not-marriage, or easy divorce, means that the state has to be involved more. Every step of the way in taking care of kids and disentangling their finances requires state intervention.
In principle, the state could leave women who had kids without husbands to sink or swim on their own. In practice, though, Morse rightly says this is politically infeasible. So the current unilateral divorce system leaves society with all the obligations of taking care of the wreckage, but none of the protections that would encourage the couple to deal with their obligations themselves.
"No fault" was supposed to make marriage better, by taking the conflict out of divorce. It was supposed to apply to cases where the divorce was not contested, where both husband and wife wanted out. Now, though, it has degenerated into legalized abandonment. And you and I get to pick up the pieces and pay for the mess.