FWIW I teach in a state school, and we sometimes have students join us from private/grammar schools especially in the sixth form (and I do agree sixth formers are different). We had an incident this year with a sixth former selling vapes to younger students- they had recently joined us from a private school and had apparently done the same there, so unfortunately private school is no protection from this sort of behaviour.
I think the fact that the school got the police involved is a good sign and shows they took this incident seriously.
Your students must have mostly gone to state schools? If they have turned into decent human beings, then that surely says the state schools in the area are mostly good.
The school I teach in is a genuinely mixed comp, only comp in the rural town sort of deal- the grammar and private schools are a long commute, so we genuinely have children join us at 11 from all backgrounds. We have students go on to medicine and oxbridge, we have students who go on to work as electricians, plumbers, hairdressers etc. We have had students go onto national and even European sporting success (albeit in very niche sports).
We have a large cohort but I think that is good because e.g. the sporty ones can join a range of teams, the nerdy ones have enough people to run a dungeon and dragons club, we have thriving extra curricular clubs of all kinds, but the ones who don't want to get involved can also find their "tribe" to hang out with.
Yes, there is disrespect and swearing, but my friends who teach in private and grammar school deal with this too- the only way to avoid it is (maybe) to home school, but I'm not convinced that is desirable, and you have said it's not an option for you.
FWIW, I grew up in a similar town and went to the local comp- at weekends, we hung out with people not just from our school but also those who went to the private and grammar schools- their friends mostly lived a long distance away, so especially at 15/16/17, we all socialised (and partied) together- we all influenced each other. Now, I think one of the biggest influences on teens is what they see online.
I get that it is scary to send an 11yo into a building with essentially adult sized students, but the vast majority of them cope, and indeed, thrive.