It's depressing isn't it.
The implications are indeed, dramatic. The issue is that colleges don't want to plough/don't have (depending on the college) the massive resources required to bridge the gap. I know everyone thinks Cambridge has masses of $$$ but unless we start defunding libraries, orchestras, the Fitzwilliam museum, the Botanic gardens, the choirs, the societies, cancer research, the counselling service...we can't plough their whole budget into fixing a problem that should be fixed years before they get to Cambridge. What would a programme look like to truly bridge the gap? You can't just throw a reading list at people and say 'Go away with this and you'll know how to spot a Gospel parable or a piece of Euripedes in Shakespeare'. You'd need to take them to art galleries and masses of theatre and music. Intensive Radio 4 listening. Years of intensive 1-2-1 tutoring on how to structure arguments. Public school kids haven't all got that because they don't need it - it's been gently drip-fed to them over nearly two decades so they can make connections without needing to ever listen to Radio 4 much, and certainly not intentionally.
Also remember, supervisors' first jobs isn't teaching kids to structure arguments and write in full sentences - it's to do research. They take on undergraduates 1) to earn a bit more money (so, an inconvenience), 2) because it's part of their contract with the college so they're obliged to (an inconvenience), or 3) because they enjoy their youthful but intellectual curiosity and ability. If they're not showing 3, then it's a real pain to be stuck with just 1 or 2. So supervisors are desperately keen to admit good students, and I have had rough diamond state school candidates whom I've really liked, and taken a punt on knowing that they'll need more polishing. But if I only took those students, and the college only took those students, and the university only took those students - or if I, the college, or the university intentionally took a high percentage of those students over ones who were already showing that capability (and the capability of excelling even higher by the end), that's a massive risk. Many of them may not fly, and either fail or end up as an earlier poster described themselves - as a solid 2.1, not extraordinary. And we'd be intentionally lowering the standards overall of the emerging graduates.
Also, I don't think you can dissect the two issues of Oxbrige needing to attract good students in non-state school subjects, and state schools not producing the kind of thinkers and rhetoricians that Oxbridge wants to accept and shape in quite the way you want. Because while more state kids going into STEM than the arts (and as someone who is relatively impecunious, I will be counselling my own children to think carefully about taking a huge loan out for an English degree!), the most well-rounded thinkers have grown up doing lots of different things. So they're good English students because their school also offers Latin and German, etc. One of the best violinists in my year at Cambridge read for the maths tripos.
As I said, there are state-school exceptions here. But there were far more exceptions twenty years ago. I have not come across an 'exceptional' non-grammar kid for a long time now.
If you think I was expressing approval at the status quo, you misunderstood me. It's deeply depressing. It's why I almost break myself to send my children to a fee-paying school now, despite the fact that tonnes of the schools here being thought of a 'good' or 'outstanding' (when actually they just seem very average institutions to me, with lots of good teachers who just don't have the resources, time or funding to provide what I'm describing above). I am a Labour-voting, state-educated, normal person.
I'll come back on the foreign student question. It's not uncomplicated. But I need lunch!