I think I get your point but I'm not sure I can agree totally.
If schools were merely a reflection of the communities, then private schools should have the same results as public schools.
I agree that parental involvement can have a profound effect in the school system; the problem is there simply isn't enough of it.
Not really...private schools by definition serve a population that wants something different and is willing to pay for it...and frequently, if parents feel strongly enough about it to pay private school tuition, they are going to insist that teachers provide what they want and that their children comply with the rules.
Usually private schools have higher academic standards and stricter discipline than public schools.
By contrast, how many times have you heard of parents suing public schools (or threatening to do so) because said parents thought the discipline and academic standards were unduely harsh toward their little darlings? I'm convinced that part of the lowering of standards in public schools is due to threats of such lawsuits. By contrast, if you don't like the policies of a private school, they can tell you to go elsewhere.
I agree that parental involvement can have a profound effect in the school system; the problem is there simply isn't enough of it.
Often, there isn't. Sometimes, there is too much, of a negative nature. I frequently think that parents who worry too much about their child's "creativity" and "self-esteem" are detrimental to a school system.
A private school has a different community. Community doesn't necessarily mean just the surrounding area and people within.
The private school community would consist of the parents, students and teachers involved. Economically, they may not differ from their neighbors, but their values and goals are likely very different. It's a subset.