i have to say i'm not home schooled, but i do agree with everything that OP has said. It makes sense. The only thing that i dont agree with is the idea that children will not strive to be the best because of their friends. I dont agree with this being a valid reason for not sending your child to school, because i think that kids should actually experiance the effect that peers can have on their education. Otherwise when your children get to 18+ and perhaps go to university, they will have little to no idea about how to cope with friends who perhaps are distracting them during lectures etc. As children get older they are able to develop ways of distancing themselves from distracting peers etc, because they have developed these skills over the 13/14 year education they have previously had in school, and therefore when a situation arises where they are being "kept back" from peers, they have a little more experience in knowing how to distance themselves, without being "pushed out" of their friendship group or whatever.
Also i think that home schooling isnt good because it doesnt not allow a child to experience authority that isn't from their own parents or a tutor. This is crucial because it will give children experience and knowledge about how to act around authority that perhaps are not as lenient as a parent.