Polling is one thing but the economics on this are extensive and they mostly reject your suggestions here. Female labor force participation is U-shaped with regards to GDP (https://www.nber.org/system/files/working_papers/w4707/w4707...), once you reach the middle part of the curve it starts to increase again as GDP increases, probably because employment becomes more lucrative to women than raising children or staying at home.
If there is an effect here it can't be all that significant, if you look at wealthy countries with larger welfare states than the US most have a female labor force participation rate at least as high.
If there is an effect here it can't be all that significant, if you look at wealthy countries with larger welfare states than the US most have a female labor force participation rate at least as high.