Comment by munksbeer
Obviously there is a bigger picture in all of this. I don't know what the correct balance is, but assume that all problem kids (for some strict definition of problem) were expelled and placed in a "problem school". I highly doubt that is going to improve that child's life or attitude, but obviously it will help those at the previous school. So we end up with a large number of kids who will almost certainly grow up to be "problem adults", in many cases criminals. Suddenly the problem you solved for the first school is now the problem of society at large.
In a perfect world, most of those problem children would be mentored correctly in regular schools and given a path to a better adult life, and therefore not create a future "problem adult".
In practice, it doesn't seem to work like that, and I agree, "problem children" do cause frictions and disruptions and worse for other children at regular schools.