Well if I sent my child to the nearest secondary school, geographically, he’ll get beaten up for being bright, quiet, and working hard, all of which are despised at his nearest secondary school. Just sayin’ 👀 I’d love him to have the free education he’s entitled to and that we fund through our taxes, but sadly it wasn’t an option for us unless he was prepared to accept a certain level of violence/abuse in his daily life, so it seems we must pay twice: once through taxes and then again through school fees. ☹️
OP’s question is whether, all else being equal, Oxbridge admissions teams favour grammar school applicants over independent school applicants. Both groups are usually from privileged backgrounds. I don’t have the answer OP but would also be interested to know. I also wonder how much universities adjust for personal circumstances. Is an applicant from a low income background, who attended independent school on a 100% fees merit-based bursary, discriminated against in favour of an applicant from a high income background who got into grammar school because of their parents’ ability to buy an expensive house in catchment and pay for private tutoring for years? I don’t know.
But OP my advice is not to overthink it, if your DC do well at whichever school and are discriminated against, then they’ll do well at Harvard etc, the American Universities admissions teams aren’t taking the same approach as Oxbridge.
(Also, DH works for a top UK company who do ‘blind’ recruitment without regard to university or school name, and the vast majority of successful applicants who ace their recruitment process are coming from independent school, whether or not they came via Oxbridge…)