What you're describing wouldn't work because the interactions between the students would influence the things you're measuring. Students don't exist in a vacuum. It would only be possible if the school's students were entirely random.

Not to mention that as you go lower in rank, yes, there are fewer good students. This is pretty much inherently true (not to say that lower ranked schools don't have good students, which is not true at all, but as a percentage yes it will decrease drastically).