Any academic gains are not worth the social stunting, especially if the child is already shy.
Happiness in life is rarely based on academic achievements, but rather on the relationships we build. These relationships are built through social skills, and our interactions with our fellow man. Homeschooling severely stunts this at a very vulnerable time in a child’s life.
In at least two of the exceptions, the kids were specifically homeschooled because they were getting picked on in public school for being socially awkward.
Counterfactuals are difficult; I was far more socially awkward than most of the kids in t high school that were homeschooled, and I was in public school from kindergarten.
I think it is true that parents home schooling their kids ought not neglect social and emotional skills any more than they should neglect science or math.
School suppresses kids and forces them to conform. That's probably the thing it does more strongly than anything else. And it does it even more strongly to shy kids.
So you might've missed out on deep friendships, but maybe not. And you almost assuredly missed out on bullying (physical and emotional) and negative, oppressive social pressure during those formative years.
Meanwhile I went to school like everyone else from the ages of 5 to 18 and I still came out at the end with the social intelligence of a potted plant. Sending your kids to school doesn't guarantee they'll turn out normal - if that was true then everybody would be normal.
What helped you with socialization?
I wasn't homeschooled before age 10 or so, so caveat emptor with younger kids.