Married, do you realise how privileged your kids are, compared to most state schooled children? You and your DH are both clearly very well educated professionals, and I think I'm right in saying that you put both of your DC into selective schools so they could do triple science and classical languages. No wonder you think they they don't need the experience of a debating society, and their highly renowned headmistress doesn't think the English oral exams (the one experience all kids get of public speaking at school) is worth much - for your DC, they would just offer opportunities to show off skills that they've been supported in developing all the way through their lives, due to their background. For students from less privileged backgrounds, debating society, drama and the GCSE oral are likely to be the only opportunities they get to focus on structuring their speech, talking slowly and clearly without fear of interruption, thinking about the impression they create through verbal and non-verbal communication, acclimatising to the feeling of lots of people scrutinising them, and (most importantly) knowing that they can be interesting, entertaining, and charismatic, and that they have a right to speak and be heard. If you can't see how rare and precious that learning opportunity is for a lot of children, then all I can say is "lucky you".
I'm not much older than your DC, at least as good at my subject as your DC are at theirs (I could prove this but not without outing myself as it made the news), went to a good state school (which was sadly lacking in extra-curricular stuff and support for university applications and careers), and had the blessed good fortune to be raised by very supportive, intelligent parents who care deeply about my education and personal development. I know that I grew up with advantages which most similarly gifted children haven't had. However, applying to Oxford was an eye-opener for me. At school it was a case of "Write the Personal Statement, get feedback from teacher who went to Cambridge 40 years ago, tweak it slightly and send it off, oh and you'll have to pop a piece of your Lit coursework from last year in the post - the poetry one will do, oh yes there is an admissions test for you to do but no I can't give you any advice beyond what you've already found on Google, good luck for your interview - if it doesn't go well then clearly you'd be better off elsewhere..." The interviews were even worse - I'd never been in a similar situation before, had no idea what to expect, and neither of them bore any resemblance to the "practice interview" that had been put on for me by the teacher who'd studied a totally unrelated subject at Cambridge 40 years ago.
Despite being very intelligent and caring about my future very deeply, my parents simply weren't in a position to help - DM left school at 15, and DF went to the local university because his parents wanted him to get a degree before joining a civil service. To them, applications process = "fill in the form and post it", and it's not as though they knew anybody who could help.
WordFactory - Intellectually, I was definitely Oxbridge material. I can't tell you how I know this without outing myself, but I can say with reasonable confidence that their intake for my subject in that year must have included candidates with less demonstrable talent and subject knowledge than me (and I very much doubt that all of them went on to achieve the kinds of things I did at my less prestigious RG university). The feedback (from the scary interviewer who nonetheless gave me a really good score) strongly implied that I'd have got a place, if my first interview hadn't gone so badly. I know for a fact that my first interview would have gone as well as my second if I'd had any useful support from my school, or the speaking and interpersonal skills that Marrried informs us have come so naturally to her children...
(Incidentally, I'm pleased that I ended up somewhere different as I loved my time at university - I just get very pissed off when people say that Oxbridge is genuinely accessible to everybody who works hard, does the right subjects, and has the right kind of mind, because that wasn't my experience in the late 2000s at all. Oxford University certainly wasn't to blame, but nor was I, and nor was the subject choice available at my school/college.)