While I don't know that it would fix the problem, I have my ideas for how I'd mitigate it.

One area of attack is no-fault divorce and abortion. You can keep your morning after pill, but surgical abortion on a healthy child in a healthy mother should not exist unless the guy who had her locked up in his basement is hanging from a tree outside. Anything less than that and you have to live with your mistake instead of letting your child die for it.