OP, you are, of course correct, that students from comprehensives are less likely to apply to Oxbridge. Nobody would argue with that - so in this sense, getting in from a state school is more of an achievement, yes.
But, for those who do apply from the state sector, they are no longer at a disadvantage in terms of the selection process. I know I sound like a broken record here - but look at the stats for the last few years. The ratio of applicants to offers made is broadly the same in each sector.
Cambridge don’t look at things in such simplified terms as ‘state or independent.’ You will see the application v offer rates are broken down as follows -
comprehensive schools
grammar schools
sixth form colleges
FE / tertiary colleges
independent schools
other
There is very little between offer ratios for all of them. The most favourable offer rate is for grammar schools. The lowest is for FE / tertiary colleges.
Then there are the stats for overseas applicants, for whom the offer ratio is lower.
Offer ratios vary far more according to region or even the ethnicity or sex of the applicant (within different subjects) than they do according to school sector.
What they are looking for is a student who has ‘outperformed’ in terms of their educational / family background. Contextualisation is a blunt instrument in many ways, but it’s better than nothing.
So a student who is likely to achieve the minimum grades A*AA from a highly deprived school where there is massive disruption and most pupils won’t even stay on for A-levels, has already proved they are exceptional against the odds.
Someone with the same predictions of AAA from a school such as Westminster will be seen as underperforming relative to their cohort. They are unlikely to get an offer. From that type of school, you will need to have at least 3xA and a lot of “extras” to prove you have made use of the opportunities available to you and gone beyond expectations.
Most applicants are somewhere in the ‘middle ground’ of having attended good/outstanding comps, grammars or ‘meh’ independent schools with middling results nobody has heard of.
So all Oxbridge can do is contextualise as far as possible. They also know that parents’ educational background is a far more reliable factor in determining educational outcomes than the type of school a student attends. Which is why they ask this question on the supplementary info forms.
Having said this, Oxbridge can only deal with those who apply. They are trying to widen participation by targeting schools in low participation areas and there are schemes such as the Sutton Trust and UNIQ. Cambridge have now started a ‘foundation year’ where students from low participation areas can apply with BBB,
So what I’m saying is, the situation is far more nuanced and complex than simply “did you go to a state school or a private school.” I think you must know this OP, so I’m not sure why you seem so keen to provoke a polarising debate.