I think the reality is far more nuanced than you want to believe OP.
It’s true that pre-16, only 7% of children are privately educated. However, at 16-18, this rises to about 18%.
At Oxbridge now, the proportions of applicants from the state sector is roughly 80%. And the offer rate is proportional to that.
But look more closely. Unis all want the headline figures of “widening participation - state school offers rise by 10% to 80%!’ What they are less keen to shout about is that about half of this state school cohort are from grammar schools or other selective state schools. And there are only about 160 grammars in the country! (clustered in certain local authorities). Is this really ‘widening participation?’
And that’s before you get into the issue if schools that select by faith criteria. Or the postcode lottery that excludes people from certain catchment areas because the house prices are too high.
What happens these days is that your GCSEs and A-levels are contextualised against the average in your school. So a student applying from say, Westminster, with ten grade 8s (ie ten A*s) would actually receive a negative score for GCSE which would indeed disadvantage them in terms of admissions. This is because the average score in that school would probably be closer to a clean slate of 9s. The exact same student, applying with the same grade 8s from a comprehensive, would be considered stellar and given a very positive GCSE score because the average GCSE score in that school might be 6s and 7s.
The question is, would the Westminster student have achieved the same GCSEs at the state school? In most cases, the answer would be a resounding ‘yes’ because you don’t get into Westminster unless you are in the top 1% of ability (at least). Most of these students, could do GCSEs off their own bat at home. In fact, getting into certain schools at 11 plus is definitely more competitive than getting into Oxbridge!
Students in independents are now being advised not to mention any relevant school trips or conferences etc on their personal statements as this might mark them out as ‘privileged.’ It’s all a bit of a mockery, to be honest.
You are told very bluntly at the uni advice days that if you are applying from a selective school, a string of top grades mean not much at all. Nada! If you don’t do something well beyond the curriculum, you will not have a chance against students with similar grades from non-selective state schools (especially those in under-represented areas like the NE or Wales). It understandable as to why this situation now exists, but nevertheless it does create an uneven playing field. If you were 18 and rejected from a uni with four A*, in favour of someone who gets a contextual offer of ABB, you might feel a bit miffed. This is also understandable.