15+ years ago, that might have been the case. Now, you might find some friends in the 3-8 year old range, but then the kids just...don't do things anymore. In both suburban neighborhoods I've lived in the past 10 years, there are basically zero middle school or high school kids doing anything except playing video games and messing around on their phones from the comfort of home. School is quite literally the only social interaction most of these kids get aside from their parents, and if they didn't go to school, they'd just spend more time playing video games or on their phones.

Outside of the coasts or university towns, there aren't any "mathematicians" with kids just waiting around to form homeschooling groups with you.

My cousin homeschooled her kids, who are now finished with college. I know they're capable of using phones (one's a programmer), but I've never seen them pull one out. They're social and love playing board games, and I suspect that comes from their parents. They also socialized with other homeschooled kids, because they were part of lots of homeschooling groups.

The kids in public school are there by default; the homeschooling parents are actively choosing to raise their kids differently, and, from what I've seen, they're more likely to interact with their kids instead of letting them go terminally online or play video games.

The previous neighborhood I lived in, had around 100 townhomes, very secluded. I never saw kids outside other than walking from the bus stop. However my current neighborhood, which is a development of 15 houses, 11 of which have children. The kids are almost all doing things outside every day. Caveat: everyone in my neighborhood is college educated (mix of engineers, professors, finance, teachers, doctors, lawyers, and some other stuff) pretty sociable, and we (the parents) all seem to independently be anti smart phone, tv, etc. high school age kids do seem to go outside less, but theyre all 2 or 3 sport kids, and pretty busy academically.