It isn't "solved" in the sense that there isn't a newly found method of making somebody who stays at home with siblings all day automatically more social. But

It isn't "solved" in the sense that there isn't a newly found method of making somebody who stays at home with siblings all day automatically more social. But all the home-schooling communities I know of solve this problem by making sure they participate in exactly that - a community. This is more often that not tied to a church, but not always. But multiple (5+) families that all have the same approach to home schooling regularly let their kids go to each other's homes for different lessons etc. Then you add the church component and they get exposed to a broader number of families who also could be doing similar things. You don't end up with kids that are party animals, but you do end up with kids that are very articulate, talk like adults, can read social cues, and all things considered, more well rounded human beings than the average public school attendee. Does it always work out? No, but I'd say if you have the energy and passion, you'll get a better result. I personally don't have kids (yet) , but if I did, it would be a toss up between a good private school and home schooling.