Some of those are rosy studies designed to be rosy tho. As in, many of those studies are are as independent as cigarette company paying for research on smoking and health. Also, a lot of effort goes into insulating religious homeschooling families from any independent sight at all.
The elephants in the room he mentions is very real thing too. Fair amount of homeschooling is explicitly social/political project. It is meant to shape both how family structure looks like (who is head of the house) and also meant to create young people that change larger society into religious one. ( Partly you can see it when you listen to homeschoolers talking about public school or even non religious people in general - frankly they often sound like aliens who got the idea from movies. )
Though why the fact some people might choose homeschooling with wrong goals in mind should prevent you from choosing to homeschool your own children, with your own goals and methods, which will be different from what other homeschooling parents would choose?
Yeah, I've noticed a trend in HN homeschooling comment threads where discussion on the personal choice of whether or not to homeschool gets tangled up with discussion about homeschooling on a policy/societal level.
There are some broad concerns about homeschooling that are not relevant to individual decisions. E.g. I don't care that some homeschooling parents use it as a cover for abuse/neglect because I'm not an abusive/neglectful parent. For my child, that's not a risk factor. And as you point out, it's the same for motivational factors.
The elephants in the room he mentions is very real thing too. Fair amount of homeschooling is explicitly social/political project. It is meant to shape both how family structure looks like (who is head of the house) and also meant to create young people that change larger society into religious one. ( Partly you can see it when you listen to homeschoolers talking about public school or even non religious people in general - frankly they often sound like aliens who got the idea from movies. )