It's fairly well known that, in some villages, everyone is responsible for raising the children, not just the parents who conceived them. Over time, this process might evolve and grow, as populations evolve and grow, into the modern day version I've depicted.
I think this is stretching the reality of the situation a fair bit. In societies with very strong and consistent social norms, in communities where everybody more or less knows everybody (less than the Dunbar number), anybody can discipline children who are misbehaving. The children still have a mother and a home, and they know who that is and where it is. This will be much weaker in societies that aren't so much about the nuclear family.
I can't see any plausible mechanism to get a society with apartments and suburbs doing this though. (Meaning such a society would not develop such living arrangements, and such living arrangements would rapidly destroy such a social arrangement)
It's well written. You may have inspired me to write my own weirdtopia.
Utopia and Dystopia have something in common: they both confirm the moral sensibilities you started with. Whether the world is a libertarian utopia of the non-initiation of violence and everyone free to start their own business, or a hellish dystopia of government regulation and intrusion—you might like to find yourself in the first, and hate to find yourself in the second; but either way you nod and say, "Guess I was right all along."
So as an exercise in creativity, try writing them down side by side: Utopia, Dystopia, and Weirdtopia. The zig, the zag and the zog.
I'll start off with a worked example for public understanding of science:
Disclaimer 1: Not every sensibility we have is necessarily wrong. Originality is a goal of literature, not science; sometimes it's better to be right than to be new. But there are also such things as cached thoughts. At least in my own case, it turned out that trying to invent a world that went outside my pre-existing sensibilities, did me a world of good.
Disclaimer 2: This method is not universal: Not all interesting ideas fit this mold, and not all ideas that fit this mold are good ones. Still, it seems like an interesting technique.
If you're trying to write science fiction (where originality is a legitimate goal), then you can write down anything nonobvious for Weirdtopia, and you're done.
If you're trying to do Fun Theory, you have to come up with a Weirdtopia that's at least arguably-better than Utopia. This is harder but also directs you to more interesting regions of the answer space.
If you can make all your answers coherent with each other, you'll have quite a story setting on your hands. (Hope you know how to handle characterization, dialogue, description, conflict, and all that other stuff.)
Here's some partially completed challenges, where I wrote down a Utopia and a Dystopia (according to the moral sensibilities I started with before I did this exercise), but inventing a (better) Weirdtopia is left to the reader.
Economic...
Sexual...
Governmental...
Technological...
Cognitive...