I think the big problem is conceiving of these things as an "either/or" issue. Like to some extent any kind of "natural" social enculturation of a person is necessarily going to revolve around both a familial life & a public social life.

Like you say that

The whole “send them to school, to extracurriculars, and then home” thing is overly rigid and isolationist. As if we are meant to spend our days traveling between isolated social silos.

But this is really only an issue of like; on the one hand Capitalist demands of like rigidly structured & mandatory work-days, but also just at a basic level a problem of the actual material construction of our society; that we physically break up spaces in such a way that they effectively exist as "isolated social silos".