I went to a science and tech magnet school for HS, so there were a fair number of homeschooled kids. By winter break freshman year, you couldn't tell most of the homeschooled kids from the rest.

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.