The private schools, you have a studying environment and in public, well you don't always have that environment.
You don't always have that environment in private schools either, so your point is moot.
I have only heard of one case where a student was asked to go to a different school because his results were not good enough to go into year 12 (that person ended up with a 98+ ENTER so god knows what the school was thinking). Otherwise, many private schools would be reluctant to expel a student just because their academic record was not up to scratch. As long as their parents can keep paying the school fees the school will turn a blind eye. They want the money to build chapels and pretty new halls so that they can *look* like a private school.
This is from experience - in almost all my classes there were people who were so unmotivated and lazy that I just didn't understand why they'd continue to waste their parents' money. They were the people who got ENTERs of 15.xx and 24.xx.