This is surely part of the story historically, but not recently. Women’s labor force participation rate peaked in the late 90s in the US, while total fertility rate is down ~20% since then. https://fred.stlouisfed.org/series/LNS11300002
There could be a rubber band effect, where it takes time to get a feel for things like paying for childcare. The reaction is going to come from those who are observing what's happening to the "early adopters".