I chuckled at "pupils from all backgrounds benefitting from each other". I grew up in a dirt poor family. Some of my classmates in high school were criminal material and many did end up in prison (for murder, not weed) before their 25th birthday. Some classmates were quiet folks with ADHD, some were punctual learners who really valued good marks. All sorts of backgrounds. The only "cross background" learning was bulling lessons that the future criminals were giving to the quiet folks. Teachers were useless and powerless to straighten up the bad apples. Luckily, I correctly guessed what I need to learn on my own to get "segregated away" from that madness, so my college years were decent. My takeaway from that experience was that the cross-background learning happens only when the backgrounds differ only slightly and have something in common.
I grew up poor and have ADHD, so went to state comp. I will say that there were definitely unpleasant sides to it, but I feel like my compadriates and I have a much more rounded and grounded view of society and class than the friends I know that went to private schools. You simply can't expect someone who's never felt poverty, whether it's their own or the people they see day in day out, to be able to be able to truly understand it.
I can see how it would probably be a more difficult experience for introverts.
Funnily enough, I got bullied more by the rich kids - who knew how to push my buttons and wind me up to the point I'd lash out and get in trouble - than the poor ones.