Anecdotally, I’m seeing the “who leaves the workforce” debate happen real time with many of my friends and co-workers. Childcare availability and reliability is atrocious is some areas, and not everyone lives by family.
I have a co-worker who is a father to two young kids (first and second grade). His wife makes more than he does and her job is where they get health insurance from. They’re having difficulty with daycare (no family nearby, problems finding consistent care that doesn’t get shut down because of a covid connection). If schools are online this fall, he has said he will need to take a leave of absence or quit, because of the two of them, they need her job more.
If my husband and I had young kids, we would be in the same position as my co-worker (no family nearby, just relocated). I get paid more than my husband, and my job is where our health insurance is. My husband would be the one to quit.
That may seem to show the opposite of what I stated first about women leaving the workforce, but consider this: the decisions above would be based on income and benefits.
The fact is that women make, on average, less than men. You can argue about how women tend to take lower-paying jobs than men, but if it comes down to a situation where someone in a man-woman relationship has to quit to take care of kids, it is more likely going to be the woman.