> Kids rarely get much time to even talk to each other in grade school.
This is not true, at least in our school. They interacted quite a lot. It is not like they would had 7 hours straight of learning and nothing else, there was quite a lot of literally dedicated playtime where teachers done only general supervision.
That's true that little kids get playtime, but that tapers off pretty quickly before adolescence. You don't see 12th graders with significant time to talk and play unless they are in after school sports.
Which is kind of my point, one could homeschool for academics and then supplement with after school sports for socialization.