Replying to various things in the order in which they appeared -
Because of how Oxbridge is presented in the media, because of how social status is reinforced in the uk.
At least you're not blaming Oxbridge for that! But you're kind of saying that it's a problem that can't be solved, at least not within a generation.
hated the culture and met a lot of over confident, arrogant people who knew just how smart they were.
As people have already said, don't compare your insides with other people's outsides. Most people are wondering if they've got what it takes to be there, and are trying to prove themselves.
Is there any difference between the ratio of state school students admitted to courses which have a pre-test and those that don’t!
Ditto for Interview.
I think every Oxbridge course interviews.
As for the pre test question - you might have to make your own lists of courses with and without pretesting, but it's all there in both universities' admission stats.
Is there actual evidence that the A students who make it to Oxbridge are actually brighter / more academically successful than the rejected ones with the same grades who end up in other good Universities?*
How on earth would this evidence be gathered?
she did find continual denial of privilege incredibly frustrating. She is white, her mum is a teacher who cares deeply about her education, she grew up going on holidays (including abroad!) and to theatres/galleries/museums, she went to an ofsted outstanding school. She acknowledges all these privileges and finds it ludicrous and frustrating that kids with way more than that are often unwilling to...
Sadly this is not an attitude solely restricted to upper/upper middle class students. Has she ever met any men?
Tbh I think she was possibly being a bit too optimistic expecting every 18 year old she met to have that level of self- and societal awareness.
I believe Oxbridge when they say they want to address diversity (of all backgrounds), I just don’t think they know how to do it. Because the people who could help are not amongst them.
They definitely want to improve things. (Well, definitely for Oxford, I admit I'm assuming for Cambridge.) And yes, I do think you have a point. They've been trying for years (decades) and there has been slow improvement, but until that vicious circle is broken, improvement is unlikely to be any faster than glacial.
Or the lamentably low entry stats of Students of Black / African /Caribbean background . And reputed low application, despite, again, seeing several on our Open Days.
The stats are very exposing, and none of it is ever explained as anything other than being some factor within the student rather than the College or University.
Why say "reputed"? Sounds like you're doubting that there are low application rates from some subgroups. But as you say, the stats are very exposing and do show this.
So, what's the solution?
I've been reading this type of thread for 5 or 6 years. A lot of attacking, a lot of defending. What I haven't read is much in the way of concrete action that could be taken to improve the situation. Surely the Mumsnet hivemind has suggestions?
Picking out of this thread -
Visit more schools? (From 2Boys) They all have their linked areas, but some colleges may be more or less active than others, so increase levels of engagement and improve consistency?
Not sure there are any others tbh, unless it's to somehow stop 18 year olds being loudmouth dicks 

Other things I've thought of -
Improve transparency re application process (flipside is perhaps that you make it easier to prepare for, which gives an advantage to those who have more preparation anyway?)
Increase engagement e.g. on The Student Room (I know there is some official engagement, but it doesn't seem to be consistent across all colleges), here perhaps, anywhere else relevant
Get someone like David Lammy who has spent years attacking Oxford for not being transparent about their possible biases, to now show his support for their effort to improve under representation?