I went to a grammar school in the 70s and 80s. I'm from a FSM family and had no coaching although others may have.
The benefits were no-one was bullied for being a nerd or a swot. There was no disruption. People actually wanted to learn, they were enthusiastic in the subjects taught. Teachers could teach at a much faster pace, go into far more detail. No-one got bored. I loved it. The school turned out a lot of scientists, doctors, vets, teachers, dentists.
My ds was bored stupid at primary school. By year 6 he was already angry and alienated. I looked at our catchment senior school but it had a 41% pass rate for boys for GCSE maths. It offered no choice of languages in years 7-9. it had no library. It just wasn't going to be enough for DS. I spent most lunchtimes in our library just browsing. The internet doesn't prompt that.
So although I'm a single mum, DS goes to the local independent - half fees, half maths scholarship. He is happy and absorbed, his maths is better than mine at 14. If I couldn't offer DS an education at least as good as I had, I would feel like I'd failed him. Even if it costs me my pension.
Grammar schools should be for the nerds & swots. They are not a social statement or something to coach for. They do not make other schools or pupils less valid. They should be for those who genuinely want to spend their time researching the bacteria growing in the boys changing rooms 😀
Grammar schools are not the problem, it is people's attitude to them that is wrong.