I have no idea, it's very interesting though! I have no skin in the game - my daughter has left and I have no other children to send there or to any other school. With respect to the original question, though, I don't think that a girl in what has traditionally been a boys school is going to get the best sports opportunities either.
I don't really know what you would do in a school to encourage brass players. I know SPGS and probably all other schools of this kind offer taster lessons for shortage instruments, but not sure how you get kids to give it a go if they are not interested. One of my best friends at SPGS played the french horn to a very decent standard and the orchestra had at least sufficient brass players from the school population which I think you said was no longer the case so not sure what has changed there. I do wonder if it's a societal thing in that gender roles and expectations seem to have become more entrenched rather than less since the 80s and 90s. Maybe brass is seen as a boy thing? I don't know.
With regard to career opportunities in sport, I'd have thought that either a private school which prioritises this (Millfield or somewhere) or a good state so that you have the time to devote to whatever sport you love might be much better options if you are someone who finds this a realistic prospect rather than somewhere where you'll be doing more subjects at GCSE than most people and you're going to be expected to be doing very well in pretty much all of them. I don't think sport as a career really features in most SPGS parents' thinking though I know when my daughter was at the school, there were a number of children doing pretty well in various things including being in national and county teams. Don't think any of them opted for Ivy League, they've all gone to Oxbridge or similar as far as I'm aware where sport will be of little relevance in the vast majority of applications though I'm sure they will continue to pursue their own interests.
Parents are certainly hoping for top universities for their children at all of these schools. But nobody who is applying in the UK will care about sports - Oxbridge explicitly states that it doesn't care about extracurriculars. It's all about grades, personal statement and super curriculars.
I remember someone complaining about SPGS maths too, which really surprised me as they tend to have a lot more girls taking maths and science than any other school of a similar type. I think more than half of the year take maths generally. But it's very common that people have a sort of need to criticise the school, often because they are a bit scared of the reputation and don't really understand the ethos or how it actually works.
I do think that SPGS encourages girls to find their own academic passions. And I was very supportive of this as a parent because I don't think people should be pushed into studying stuff or doing particular sports because their parents think it's a good idea. Children should absolutely follow their own passions and interests.
It's a very interesting area. Wish @stringseleven would explain what other schools are doing differently because I am genuinely interested to know. As I said before, it's all in the past for me and we have finished with school. I just find it interesting.
Sorry! V long.