OP, I'm a Cambridge grad, was the first (and still only) person in my family to go to Oxbridge.
What I observed while studying there, is that the 'Oxbridge type' really thrives under pressure (8 week terms, essay each week, etc) and typically also gets a lot out of the extra curricular elements (I did a lot of theatre, have good friends who did the sporty thing, etc).
Lots of phenomenally bright kids apply and don't get offers because the interviewers have correctly identified that they would not suit the hot-housing environment.
Rarely, one of those applicants gets offered a place, and that's when there can be very serious MH issues, self-harm, breakdowns, etc.
It's wildly simplistic, as PPs have said, to imply that 'the cleverest young people will study at Oxbridge'. If someone in the family or school is implying this to your child then it's your responsibility to nip it in the bud, honestly.
There are many great University options and zero point in fixating on Oxbridge.