Home schooled children generally get plenty of "socialization", it's just with adults rather than with large groups of children. All of the ones I know had social skills at or above average.
And yes, socioeconomic factors play a huge part in outcomes.
I find the "socialization" argument to be one of the weakest, honestly. Being able to "socialize" in a group of, say, second-graders with one teacher to 25 students is probably worse than useless; it's a pathologically bad socialization environment for spreading bad habits and incorrect expectations created only by the schooling environment in the first place. Unless you become a second-grade teacher, it'll never come up again, and you should actively not use a lot of the socialization skills you "learned" in that environment. While better than literally sitting in a room by yourself, I can't rate it above much else, and "sitting in a room by yourself" is not actually the alternative on offer. (After all, the parents aren't going to be able to stand that either, except in extremely pathological cases which are going to be pathological no matter what.)
If the schools were set up more like Montessori schools, this argument against homeschooling would carry a lot more weight. Age-based cohorts are pathologically bad environments, and if you look at history as a whole, a bizarre exception to the normal human environment. If it wasn't for the fact that the people arguing happened to grow up in that environment and thereby consider it normal, despite how abnormal it actually is, nobody would be arguing it's a good idea.
Its not the in class socializing, but out of class. Hanging out with your friends at lunch. In the halls. Walking to and from school. If you try socializing in class you get sent to the principle for being disruptive. Meeting kids your age in your area and seeing and talking with them every day is the social aspect, not class time.
I was educated montesorri until middle school, and while there was plenty of socializing it was ultimately detrimental imo. A couple of us including me had serious trouble getting assignments done with all the distractions and were always in the principles office as a result. One kid just had to work in a separate 'office' because he could not actually get his stuff done with his friends there in the class room available to talk all day. I didn't get my work ethic up until high school, didn't really apply myself until college, and to this day I struggle with self discipline and staying focused on the task at hand.
"I was educated montesorri until middle school, and while there was plenty of socializing it was ultimately detrimental imo."
So, you went from what I describe as a reasonable environment, where you did OK, to what I describe as a pathological environment where suddenly you had a lot of trouble, and apparently mostly (but not entirely) recovered when back out in a more reasonable environment.
This is basically what I would predict with my theory. You were damaged by entry into a pathological environment. How would you be if you had never been exposed to it? How much more damaged are those who never knew anything else?
I don't think your experienced is evidence against my point... it's evidence for.
You're not learning explicit skills. You're learning implicit, semi or involuntary communicative behaviors. Similar to those not learnt by animals who cannot behave properly because they were not socialized when young.
But for humans it's more involved. We are essentially talking about a certain common cultural fabric and the problem is that if you don't fit that fabric, you will be at a disadvantage. Making friends, dating, interacting with coworkers - there's a critical window to keep your kids from turning into someone the average person would perceive as "weird". And the behaviors are subtle. Things like posture, voice tone, word pronunciation - I think "nerds" evoke a certain uncanny valley response in some people. That's a risk of homeschooling.
It may not be ideal but human nature is such that humans typically expect, on average, some degree of conformity. If personality and behavior are multidimensional vector, we're talking about an emergent clustering force, transmitted by socialization.
Edit: I speak from the experience of having spent years trying to catch up.
You don't teach someone how to play baseball by forcing them to practice wrong technique for several years.
It's not just easing them in to socialization... it's giving them wrong socialization. We're all hot-to-trot about how important teachers are for all sorts of other skills both soft & hard, but it's apparently OK for kindergarteners to teach other kindergarteners how to socialize and it'll all be just the same as if they get good socialization the historically-normal way.
I was home-schooled from the 5th grade on. The amount of socialization I got was nil. I spent the entirety of that time utterly alone. It's been nearly 20 years and I still struggle with social stills. I'm strongly of the opinion that home-schooling your kids is one of the worst things you can do to them.
Based on the parents I've known who've homeschooled, I suspect the lack of socialization you describe must be at least a little exceptional. Not to minimize its impact, but it doesn't seem like a necessary consequence of the practice, going by what I've seen.
I wasn't home-schooled quite as long (5th-10th), but this was basically my experience too. We did go to outings with the local home-school group, but the local home-school group was 90% children with autism whose parents didn't feel the local school system handled special needs well.
And yes, socioeconomic factors play a huge part in outcomes.