Yes, and so are public schools. And a few school dropouts have also done quite well in innovation and leadership. The down side of private schools is that the cost prevents most kids from getting in.
Anyway, it's really more to do with the person than the school. A talented person who gets good schooling is better off than a talented person who gets little or no schooling, but even the best schools can't make something out of inferior kids.
As a society, it would make sense to send our best kids to the best schools, regardless of whether they could afford them or not. But we don't. So we waste a lot of potential talent. 8-<