You got it all right and I agree with you. I also blame our governments you putting us in a position where we cannot provide for a child on our own; not having proper social programs to assist people who are sick and need time off; and overall creating conditions when many cannot have children.
I'd say the best thing the second parent can do if going back to work is economically unsustainable and illogical is to start a business. Paying business taxes when you have a corporation is easier, and you'll be in a lower tax bracket unless the business explodes. But the fact that someone in the family has to leave the conventional workforce and make sacrifices while the other one is advancing their career is awful. Imagine offering your partner to switch every few years so that your career doesn't stagnate? I imagine their reaction wouldn't be great.
You're right about most women not seeking to be parasides. I only mentioned it because I've seen such examples in conservative communities and the country I grew up in.