I agree. Public school is not a great place for socialization, and it's not hard to create something better. Nothing socializes kids like sitting next to each other motionless in silence for several hours lol
It's not about getting your kids to form the best relationships possible, it's about teaching them to be comfortable with and learn to handle a huge swathe of people that are different from themselves.
And, possibly more importantly than that, it's about teaching kids to do this without the immediate presence of their parents.
Are public schools a perfectly diverse cross section of the population? Of course not. Are they a whole lot closer than very nearly any private school or home school? Absolutely.
Homeschooling brings you into contact with a self-selected subset of the population, but across much wider range of ages.
This often turns out to be more broadly valuable.
that possibility isn’t even in the range here
the choices are good school district, decent private school, or a home school concept
No amount of artificially constructed socialization immersion is going to beat the organic development of spending several hours, every day, surrounded by a ton of other kids.
What you end up with is a kid who has marginal experience with conflict resolution, communication skills, and any degree of independence. Which in turn, makes them perceived as weird, meaning that when they do have social interactions with others, they get marginalized, and further deprived of social development.
Public schools definitely have a misalignment of interests problem, but private schools solve that problem without stunting your child's charisma.
Selecting relatively obscure sports that nonetheless have a decent representation on college sports rosters is a college admissions and scholarship “hacking” thing. Fencing used to be a great choice for that, dunno if it still is.