My dad calls it the pay-your-neighbor-so-he-can-pay-his-neighbor phenomenon. Uncle Sam makes the most money in that relationship. He makes nothing when you babysit your own kid; he makes plenty when you hire someone to do the same thing(and someone hires you to do their thing).
This isn't politics. It's a simple fact. You stick out 5 years or so with very expensive child care (maybe 4, for many families, where someone stays at home for the first year), and then two-income families make sense again.
And since you've fostered relationships with the parents of your friends' children (or fostered your childrens' relationships with your friends' children) odds are there will be enough overlap in after-school activities that rides home are equally simplified.
Of course, this sort of stuff does take planning and relationship building, but generally it will be a lot less trouble than having a single-income household.
It seems fraught; taking care of someone else's children is a serious commitment. If you screw up your schedule, people lose half a day of work. After-school child care just isn't expensive enough to be worth this hassle.
I believe that high taxes would rather put a stop to the one-earner household since marginal effects on two incomes at X is usually a lot less than the tax on one income of 2X.
Is subsidized child care, really cheaper - if you are paying higher taxes to receive the subsidies? Kind of an odd logic.
Also, as you are growing up, the parents typically make a bigger investment than an average parent. I never have to "repay" my Dad any loan. Nor does he need to repay me. Does it all balance out in the end? It may or may not; it's pretty irrelevant.
My mom gave up practicing medicine after her first kid. She never really had to worry about not being able to return because she didn't plan to.