Another diet to experiment with is the No Starch Diet. There's a lot of anecdotal evidence suggesting that starches somehow trigger an autoimmune reaction in some people leading to Ankylosing Spondylitis and possibly others like Irritable Bowel Disease.
It's not an easy diet to follow, but the food test is simple - red iodine turns blackish blue in contact with starch.
Any reform involving private schools in the US needs to be wary of its effect on ideological and cultural divides. We already prefer to live near like-minded people, it's not a stretch to assume we'd send our kids to like-minded schools.
To be more specific, we don't want our school system to become a proxy for culture wars - individual schools marketing themselves to parents as a place which builds proper (liberals|conservatives|tea partiers|greens|etc).
No matter what shape reform takes, society needs to make sure its people get a well rounded education.