Women got the vote in the US early in the 20th century. They started entering the workforce in great numbers during WWII. It is a fact that they become more independent and less dependent upon men. The welfare state had very little to do with it.
This is a worldwide study. Notice that Chile, Costa Rica, and Mexico have three of the four highest out of wedlock birth rates. Do you think the huge infusion of Mexican immigrants, legal and illegal, contribute to our 40% rate?
The chart you presented that compares 1964 to 214 shows the destruction wrought by the adoption of a welfare state in the 1960s ... long after most of those countries made the mistake of letting women vote.