"And actually I don't want comprehensive. I think trying to be all tings to all men is a recipe for under achievement."
What - you don't think that the best comprehensives in the country, those which have a representative number of very high ability children, those which are well resourced and have a good record of improving outcomes for the full range of children they take in, just simply aren't good enough? Because they are comprehensives trying to be 'all things to all men'?
"don't assume that the calm and harmonious atmosphere is all because the difficult ones have been booted out, That is not always the case"
No, indeed. But it's USUALLY the case.
Yes, private schools do accommodate children with special needs. What they don't do is accommodate children from very poor families, where there is inadequate parenting and a deep disrespect and disregard for education. It is these children, more than children like my DS (who has ASD and is in a state mainstream), whose behaviour is generally the most damaging.
OP - I have a suggestion: that the most socially disadvantaged, disruptive, unsupported and difficult children (not necessarily those with diagnosed special needs) be given bursaries and accommodated by private schools.
That would take the burden off the state sector and would provide these children with the wrap around care and pastoral support that they really need that private schools regularly boast about.