There's a lot of success stories, in my own family while I was not homeschooled my younger siblings were all way behind where they were supposed to be academically when my parents adopted them and they got caught up via homeschooling. I also knew some people in the military who were homeschooled who had good things to say about it.

The problem is that a lot of homeschooling in the US isn't done because the kid has special needs that the public system isn't accounting for. In fact most of it is done strictly for reactionary reasons. Usually religious, sometimes secular, always batshit. Extremely controlling parents will choose homeschooling to limit their child's exposure to outside influences, and that's where a lot of the horror stories come from.

From my limited knowledge it seems like the secret to success is having a network of parents working together, forming a kind of school district of their own, and for the kids to be enrolled in outside activities so that they interact regularly with their peers. As with everything it helps if you have money, good luck homeschooling if you need every working hour you can get to make rent.