This isn’t a surprise, because independent schools hothouse children to ensure they peak at a levels, whereas what universities want is students who will continue to improve at university.
I have two children (3xA*, 1A for one and 3As for the other) who were not interested in Oxford or Cambridge. My experience of Cambridge students (I live in Cambridge) is that I have seen many burn out. You also end up with a very narrow program of study which for children with broader interests forces them into a box very early. It’s also a 3 year undergrad program with 24 contact weeks a year, which is insanely short.
My children have gone to Scotland (Edinburgh and St Andrews) which allows significantly more flexibility than English universities offer in choosing subjects outside your chosen degree pattern. St Andrews even lets you change degree completely if you find something else you like.
If you really really want to be a mathematician at 18 then I can see why Cambridge or Oxford might appeal; for kids with more breadth, I think it’s a poor choice.