There were fewer universities and fewer students. Those who didn’t want to study further got a job instead.
Almost. In actual fact what happened was that there was very little support and nothing in the way of dispensation or specific support 11-18. Therefore, by the time you got to university 35 years ago (source: was at university 35 years ago) anyone with the slightest predisposition to not cope had been filtered off. A Levels were norm-referenced up until 1988, there were for practical purposes no arrangements for extra time / different modes / etc, there was very little continuous assessment and examinations were entirely terminal. In essence, if you could get through A Level, you could get through university: it was absolutely standard to say that A Levels were the hardest and most challenging exams you would ever take, which is I think no longer true.
Not only were parents not involved at university (with some pretty nasty consequences, as MillicentF says) they were much less involved in education throughout, in part of course because if you were at university in the early 1980s your parents were born before or during the war and therefore it would be rare for them to have a post 18 education, and even rarer for them to have gone to a to 3/4 year live-away university. That all adds up to arriving at university at 18 in the early 1980s as being a pretty good mark that you would cope. That's not a system to look to return to.
“rates of mental illness at Oxford or Cambridge (very high, and rising), rates of non-completion at Oxford or Cambridge (very low, and falling)”
That doesn’t add up. Are you saying that the students who are suffering from mental health problems don’t drop out? Is the pastoral care really good there?
As an analogy, consider the Tour de France. Are rates of injury and illness high? Yes. Are rates of completion high? Yes, all things considered, particular the completion rate of stages. Is the long term effect on the health of the athletes positive? Er, no. Oxbridge's support systems are good at getting students, who have already been pre-filtered to be tough, smart and motivated and also have been pre-filtered to have parental support, through their finals. They do that amazingly well. Just as Tour de France doctors are good at putting people with serious injuries back on their bikes to finish the stage.
Oxford and Cambridge have high rates of mental illness, but amongst students who are absolutely focused on, and committed to, completing. Other universities have lower rates of illness, but students who are either less committed to finishing, or who drop out for other reasons (academic, financial, personal) which don't affect Oxford students as much.