Putting the dumb kids in one class would only pigeon hole those kids. They would be made fun of at school, and systematically taught that they are not as good as the other kids. Whoever ends up teaching "the dumb class" would naturally have low expectations for these supposedly helplessly dumb students, and as we all know, teachers teach worse when their expectations are low. So your plan would help the kids who are already smart, while ruining the lives of kids who need the most help. Hell, many times putting a very dumb student in a class full of smart students improves the dumb student's grades, because good study habits rub off on them.

This is only true if segregation is done by age as well as by ability. If a third-grader is in math class with mostly sixth-graders, history class with fifth-graders, and Spanish class with mostly first-graders, he's not going to think, "Oh, I'm a hopelessly dumb kid." Likewise the sixth-grader who's in Spanish class with mostly third-graders, history class with fifth-graders, and math class with fourth-graders isn't going to be stuck with a bunch of people with no motivation and no study skills. He's going to be surrounded by students of all types--some of them very bright, some of them not so bright--but who all have a solid grasp of the prerequisites required for the material at hand.

Unfortunately, it's a bootstrapping problem. If everybody is in classes with people their own age, then for one person to be "held back" and put with younger kids (or to be advanced a year and put with older kids) is a social disaster. But if every class has a wide range of ages to begin with, there's not such a huge stigma attached to being one of the older or younger kids in the class.

The only problem with competitive schools is that for competition to work, you need to have schools that lose. And that means that the students lose.

What? You have a weird idea of what competition means. Does having competitive grocery stores mean that some grocery stores win and some grocery stores lose? Which means the people who go to one grocery store get crappy, spoiled food?