>>Surprisingly hard to expel a child, particularly in the more privileged schools

In my experience - it's the reverse. Expensive private schools were quick to expel students because as much as they liked the money they liked having good academic results they could boast about much more. It's the basic run of the mill public schools that can't expel anyone because the student has to be in education somewhere and they might be the only school in the catchment area, so there are no good alternatives.