I'm wondering: Do we understand the long-term impact of this lack of "social school" from how homeschooled kids do post-education?
In standard school, there are very rigid age-based hierarchies. Sixth graders rule over fifth graders, who rule over fourth graders. And the adults rule over all of them. And then you have the cliques, etc.
You'll find that such hierarchies do not exist in the homeschool world, and the kids are better for it. If the homeschool environment is religion-based, you'll probably find that the children do not know how to interact well with people in other religions, but you still have excellent interactions between age groups.
They all did pretty heavy extracurricular activities. Keep in mind that i met them in a particular time, either as a youth camp counselor or as a "street educator" (not really, basically i animated open physics classes with experiments/construction for kids, think Kiwico but free and with social settings).
They also were quite late in STEM, even those with engineers parents (definitely not the majority), but at least bilingual (i saw a 10 year old girl speaking 4 languages and playing violin better than i did). The most "advanced" i saw (at least in mathematics principles and understanding) where those with a formal musical education. Most of them could play at least one instrument, but those who understood underlying music principle were definitely more likely to "get" physics and engineering for some reasons. I think pattern recognition is definitely important for people to understand STEM work, and that can explain my limited, anecdotal data.
Another common point is that each of their familly were fairly religious (or spiritual rather), but not close-minded. I think around half were christian (not really defined), and the other half were more new-age. No Chomsky day for any of the famillies.
[edit] It's quite unfair from me, putting them in boxes like christian and new-age. Let say around half of them believed in a single entity we could call god creating the universe and guiding humanity, and the other half believing that the universe himself (or Nature, or the soul) guide them. I'm pretty sure one couple were active dualist proponents
Maybe these traits are specific to Christian homeschoolers and not homeschoolers in general, but frankly I have never met someone who was homeschooled because of secular, rather than religious reasons.
IME, the homeschooled people raised by people (homeschooled or not) to whom that description does not apply also do not tend to fit it, but people to whom (again, homeschooled themselves or not) that description does apply are overrepresented among those choosing homeschooling for their kids.
These last two years have changed my perspective. While the vast majority of people were bathing in hand sanitizer, hoarding toilet paper, locking themselves away in quarantine, and avoiding elevator buttons, the people who were least in tune with popular culture (Religious, rural, etc.) seemed like the most rational actors. In my opinion turning off the TV and ignoring mass media, sports, culture is probably the most healthy thing a person could do.