As the OP appears to have a rigid fixation on Oxford and Cambridge and an inability to see shades of grey, I’m not sure anything other than blunt responses are likely to get through, are they?
As for the Oxford and Cambridge admissions systems, they definitely result in far more emotional investment from candidates, which is unhealthy if you are not mentally and emotionally robust, but I don’t think it makes sense to argue that their selection system is somehow more opaque or unfair than any other university’s. Imvho, it’s opaque and partially subjective that the same candidate should appeal more to any university than another on the back of no more information than what goes into their UCAS form and what their postcode is - same candidate, same information, different response. It is, basically, clearly not the case that other universities’ selection criteria are 100% objective, although the less popular the university, the more likely it will be that it can just make offers to 100% of people meeting set statistical criteria, none of which are based on subjective references from teachers, partially subjective grade predictions, or another human’s subjective opinion on any part of their personal statement.
Oxford and Cambridge provide far more information on how they assess candidates than any other universities in the UK, and gather far more information about the candidates in order to do it. There is also detailed information provided in what they are looking for at every stage of the application process, and scores of example Oxbridge college interviews on YouTube for anyone to watch, should they be wondering what to expect from that part of the process.No system is perfect or free from all bias, but there is something badly wrong with the notion that unless you can’t see or hear the candidate, and can’t read anything they’ve written, you are creating a subjective and unfair selection system because any evidence you receive you might not treat wholly “objectively.” And, tbf, it’s not possible to be objective about truly original thought, anyway, because there’s no pre-agreed marking system for something you’ve not yet thought of, is there? And it seems perfectly fair to me, if your teaching method is based on oral, face to face discussion, that you should want to test out that process with someone before deciding whether or not it is an appropriate method for them, because it’s not a common way of teaching pre-university and it doesn’t suit everyone.
And finally… as with any university, job, or other kind of application, you win some, you lose some. It’s far better to try and fail than not to try at all, if it’s something you think you want, and regardless of the result, it will have been a useful learning process. It’s really not the end of the world if you don’t succeed at it, it’s just more likely to feel like that for a while if you know how close you got, “yet no cigar.”