I can't honestly say what kind of girl would thrive at SPGS because I can only speak from my own experience and there may be other types who would enjoy it just as much as mine, IYSWIM. Certainly there were a massive range of girls in her Y7 form and they were not a homogeneous type at all from what I could tell. They all seem to be happy so far.
But mine is relentlessly curious to the point of completely exhausting me even now she is 13 (it's like toddler questions that never end only on a higher level and I have found myself saying 'I'm not sure I care or want to know' at times which obv is not my finest parenting moment), really loves learning, very quick to pick up on things (I don't mean to learn things as such, more to make connections and extrapolate, sometimes too far which can end up in anxiety - which they have helped her with enormously). She's a bit of an odd child in many ways, very much an individual (which probably means a bit of a weirdo) with an iron sense of self-determination and a strong and active dislike of being put in a pigeonhole or complying with expectations that she cannot see the point of. She is very much a petition-starter and mini-activist and spent her entire primary schooling railing at what she saw as pointless rules and regulations. At the same time, she's extremely compliant with adult expectations, as long as she can see the point of them.
She's got a very strong sense of social justice, is v v engaged with politics and world issues, is extremely moral to the extent of pissing off nearly all her peers at primary but has found strong, nurturing and happy friendships at St Paul's despite being quite introverted and someone who has struggled with friendships on a number of levels previously.
I don't know what the Oxbridge process is like now. But I went through it myself and didn't notice any pressure particularly. It was all just 'oh, why not give it a go'. Things may well have changed in the intervening decades!
I agree, these are all good schools and they all have their good and bad points. But I thought DD would have been very unhappy at most of the other schools I looked at and was pretty sure she would love St Paul's. And she does. She really really does.
I didn't, by the way, really choose the school because of my aspirations for DD, though obviously I hope she does well and gets to do whatever she would love most in life. I chose it because I thought she would fit in and be happy there (as well as some specific curriculum stuff). She never really fitted in at primary school and was unhappy quite a bit of the time as a consequence. I felt like some of the other schools were perhaps more focused on looking for those children who fitted in more easily. That would not have worked for DD. She needs somewhere you can be different and it's still OK.