I am actually fairly uncertain about this issue. I teach in a very ordinary school in Scotland and we have had an applicant penalised at Oxbridge interview for not knowing the A Level syllabus. She had very, very good grades but in Higher and Advanced Higher, not A Level. She, perhaps, should have been cut some slack and given help, by the College, with preparation.
However, I am concerned that ex-private school pupils, aged 18 or more, now adults, are, potentially, being penalised for choices made by their parents when they were 5 or younger. There is something inherently worrying about a system that seeks to select adults based on the choices made, years before, by other adults.
However, my pupils are very disadvantaged by geography and rural deprivation is an issue. They are never going to have the confidence of pupils from much larger schools. They struggle to be in sports teams and do clubs as very few of these are on offer here. All the extra tuition available in bigger places does not take place here - there are no tutors, only the teachers. Some subjects are single teacher departments which means that progress and performance are often down to a single person's input, something that can go on in a subject for many years.
And yet, although no Oxbridge success so far (probably not helped by the fee situation from now on) we have had several pupils achieve 1sts from excellent Universities. They, presumably, would have made Oxbridge material. Indeed one was offered an interview at Cambridge but did not go as she was concerned about travel costs.
So, I can see this from both sides. However, whatever the current situation is, it is not working.