I agree, grammars and faith schools, private tutors (in my area, it's only the catholic schools that ppl are clamouring to get into. The worst school in the area is a C of E secondary) are part of the problem.
Private schools are a big part of the picture too though, let's not pretend otherwise.
I'd argue against catchments for the best schools being in the most expensive areas though. In some cases, yes. In my area, no. I don't live in an expensive house in an expensive area and my child got into a lovely secondary school, it's very sought after. Birth rates in my area are decreasing. Last year she wouldn't have got a place. This year she got a place and there are 2 spare places in her form!