A-levels (and equivalents) are the accepted entry route into Higher Education. Any other selection method should be transparent and fair. It should not be up to admissions tutors with their own agendas, assuming things about families, schools they know nothing about, areas they know nothing about.
We, as a family, do very little in the way of extra curricular because we can’t afford it after paying school fees. If they went to state schools, then we could and they would then have all the opportunities you can imagine.
As it happens, my kids haven’t come across anti private school bias.
For example, DC4 received an AAA offer from a RG university. A few weeks later, they reduced it to AAB, then a few weeks after that, reduced it to ABB (no intervention from her at any point).
The other thing to remember about independent schools is that they aren’t all exam factories with gifted children. There are plenty of schools that cater for students for whom life is a serious struggle and getting to the end of sixth form is an achievement in itself. Where are the contextual offers for these students?