In fact, they can't even accept students based on grades, there are only 4 criteria they are allowed to use when selecting students: location, time in queue, siblings in the school and whether you went to pre-school there.
So what you end up with are students with parents that have enough forethought to put your name down early on.
> You can't "optimize" what's essentially a service institution.
I'm not sure what you mean by this, obviously you could in theory most definitely optimise the education. That is what private schools here in Denmark tend to do.
- The schools get a fixed amount of money per student.
- The single largest predictor of school success is education level of the parents.
- most for profit schools are in areas with higher education.
But it is still the case that a lot of the students will not be local, and the majority of the local kids will not go to the school, they will go to the local public school.*
The main reason these schools have better students is that you need to make an active choice to go there, and you need to do that a long time in advance. If you don't, you end up in a public school. This of course means that students from more motivated households go to these schools. Not wealthier students or even necessarily smarter students.
* There have been cases recently where it seems that the private school has bribed the public school system to close the local school, but in general the public school will remain and most of the local kids will go there.