Good points all, but I think it needs to be said that home schooling as it is currently practiced is often far from ideal too. The current population of home schooling parents is a self-selected group that has strong opinions about how things ought to be vs. how they are, and this ethos matches perfectly with the underpinnings of religion, so it’s no surprise to me when I observe most home-school parents indoctrinating their kids with the current religious fads … such as creationism, an invisible man in the sky and pathological body shame. These ideas don’t lend themselves to the happy, well-adjusted, well socialized people you imply. What I mostly see from home schooled kids is standoffishness. They’ve been taught to shun and distrust everyone outside their little clique, because only their group has unique access to The Truth, and all the rest are sadly mistaken at best, or evil emissaries of The Devil at worst.
If the government school system could be done away with entirely, everyone would be pushed into finding (and creating!) innovative alternatives, so the selection bias would disappear, but in the meantime many of the home-schooled kids are getting fed an even more toxic broth of indoctrination.