The socialization argument is nonsense. Schools as factory farms came first -- with no regard for socialization -- then the socialization argument was made later to rationalize it.

Forcing kids (by constructing their environment in such a way) to have only relationships with kids that are precisely the same age as them is weird. Some healthy relationships with people who are a few years older in positive. Older kids/people need to be embedded in the social circle as role models. You get less bullying and should get faster social development. Homeschooling done right is more similar to how kids developed socially in our ancestral past (all the way up to a few hundred years ago). It's also more similar to how kids develop in much of the world outside of the West where larger family units are more tight knit.