No skin in the game here.
I agree you can’t just line up percentages from selective and non-selective schools and call it a straight comparison.
But I also think it’s WAY too simplistic to say “top sets would be the same apart from drama and facilities.” It’s not just about music rooms and theatres.
Take something practical: schools like St Peter's who have around 1,300 students on site. Tormead School (and tbf most privates) has roughly 800 across the whole school and if you look, with (give or take) the same level of staffing. That inevitably changes day-to-day experience, class sizes, access to teachers, access to extracuricular/clubs, academic provision, space, sport provision, how quickly pastoral/academic issues get picked up.
Tormead (simply in the spirit of this tread being about Tormead!), for example, also has its own dedicated sports grounds and hockey pitch, alongside onsite facilities, and generally much smaller classes (at A-Level it can be 1:5 in a specialist class). That’s 110% not a criticism of state, i'm a product of state and did well for myself, but, it’s just maths. Fewer pupils per teacher and more resource per head does create a different environment, it cannot be denyed.
And yes, plenty of very bright children in top sets at George Abbot School or St Peter’s will achieve excellent results. Incidentally, St Peters have improved their A-Level results since taking swathes of Tormead (plus other local girls schools) Girls for A-Level, the ones who wanted co-ed or to save some £. But they’re still within a much larger, mixed-ability system. A fully selective cohort changes the academic dynamic across every lesson, not just the “top set”.
What happens is OPs daughter doesn't quite make the "top-set", does she still achieve as well in a very mixed ability second or third set? At most (smaller) independents, value-add is very high, so outcomes outside of "top-sets" is proven in studies to be better.
On sixth form: absolutely, 100% agree, some girls choose somewhere like Godalming College for co-ed or independence reasons. That’s simply a lifestyle and preference. But academically the A-level outcomes aren’t the same, so it’s not quite accurate to say everyone (note I said everyone!) “ends up in the same place.”
It’s not about state being bad and private being magical at all. It’s about acknowledging they are structurally different environments and that difference goes well beyond just music/drama studios.
As a simply side note, my (only mildly) SEN DD struggled in state primary, large classes (31 I recall), got lost, almost labled as 'naughty', etc. We took the decision to borrow and send her to independent, and the provision was light years ahead, she flourished.
It's horses for courses.