As someone who had a very diverse primary education including 6 years of homeschooling, I can tell you OP here is very on the money. Without going anonymous I won't go into much further anecdote, but I can tell they actually experienced the lifestyle.
Maybe there are some "well adjusted and normal" home school groups out there, but I never encountered one. When you talk to these parents you will only get the social proof they want to hear - the parents are absolutely having positive social experiences. Perhaps delusionally so. Especially the types of folks drawn to home schooling to begin with.
I'm not saying it can't be done - but that blocker should be big because it's often simply talked around and the parents saying their kids were well-socialized often are saying it only from their perspective. I too, have seen much more estrangement from parents from my home schooled vs. other friends and it's not remotely close.
I think it's primarily a form of self-selection. Perhaps the pool of parents selecting to homeschool after COVID has changed considerably since prior to it, but I'm skeptical. It takes an exceedingly exceptional and dedicated parent (and probably child) for this to work out in the end. There are anecdotes out there, but they typically to be of the "very upper class" kind where a kid is exposed to university level educators at a very young age.
"I run a company that helps families interested in designing their child's education as a replacement or supplement to traditional school."