Bertrand you really do talk complete bollocks much of the time (sorry, as I said I dip in and out so this is in relation to a comment a long way back). Work experience for DC at our school is not 'always (or indeed usually) in merchant banks or gleaned through nepotism as your DD's was. You just chuck these things out with absolutely no basis in fact.
On another point, As might make a huge difference to what path a young person's career might take. My own DC are a case in point - they'd all be on a very different career trajectory without them. Certainly my eldest DS couldn't have got into Oxford to read Medicine to pursue what has genuinely been a lifelong ambition to be a particular type of doctor without them, since that course requires, among other things a minimum of around 9A.
On the Classics point. Classics is an excellent subject in terms of training the mind, as is Chemistry or Maths. I can't see why the country should be governed by STEM graduates!