To revert to OPs post I think schools like Eton and Winchester have such a long tradition at the centre of the British establishment that it leads parents to develop the sort of zeal you refer to.
Women have never been at the centre of the British establishment, let alone women from certain schools, with the possible exception of SPGS and it's procession of the daughters of the political and intellectual elite. Secondly, again with the possible exception of SPGS, few girls' schools have a long history of being destination schools. The league tables for girls' schools, and indeed leaver's destinations, even fifty years ago were very different (some of the schools then top do not even exist now), let alone 100 or 200 years ago, and of course though often led by blue stockings who had themselves broken the academic glass ceiling and encouraged female empowerment there was still a lot of girls in those schools looking to more traditional female role models. Even so, though SPGS does have that history there is still a sense of it sitting uncomfortably on it's perch as was manifested in the recent thread, partly because it is not so confidant in it's skin as to not be implicitly constantly striving to be at the top of the league tables (leading to parental dissonance with what is on offer / the school's resulting reputation). Winchester and Eton are not afraid to do their own thing in terms of selection and education even if it costs them the top of the league tables.
Molio and MN164 Having experienced DDs at both very selective girls' schools and very selective coed, and know DDs at Boarding Schools including WA, and had intimate contact with girls' with eating disorders and mental health issues I would say there is an element of truth in what both of you say. I do think those issues very much orginate in the family background and there may be a correlation between the incidence and very selective girls' school because those are the schools that competitive parents (not saying that those issues exclusively orginate with competitive parents but most girls with those issues in selective girls' school do come from backgrounds where the self indulgent parental behaviour is the root cause of their insecurity) tend to choose. The incidence of these issues in those schools is not so consistent as to suggest that the school environment is the main causal factor, in one year there was one girl with issues, in another ten had been treated at the Priory by Year 9. Of course hearing that will instantly confer a reputation on a school. What I do think is that in a year with a lot of girls' with issues, an all girls' environment can amplify the problems. It is easier for attention seeking insecure girls to manipulate group norms and foster a dysfunctional environment in which there is exclusive, disruptive and indeed predatory (in terms of the opposite sex) behaviour, with resultant misery for all there, but only if there are enough of them to overcome the values and norms of the other girls. That sort of behaviour happens less in co-ed schools. The presence of boys is as much a civilising force on girls as their presence is on boys, and the extremes of their behaviour.
However we have also experienced the benefits of being able to thrive academically in an all girl environment, it is right for some girls. Sadly some boys do seem to absorb the values of patriarchy early and seem to need to have an upper hand / dominate the dialogue, especially in STEM subjects. For some girls it is better to be inspired and develop the academic confidence away from that environment so that they can emerge ready to tackle it in the real world.