I trained to teach, not be a careers adviser, and every teacher has to have a degree.
I think it's insulting to say they can't teach the syllabus. At KS3, it's not hard to teach the syllabus, and at KS4 it's perfectly doable. A level is harder, and I think every county should have specialist sixth form colleges, as they do in Hampshire. Teaching A level is a different ball game altogether.
If you have sixth form colleges, then you can staff them with the correct careers advisers, and liaise with Oxbridge colleges.
As for advising about high paid careers, not every one wants one; not everyone wants to leave their part of the UK and move to London to live in a cramped room whilst making their way in the City.
Arguably, with information now so freely available, most kids have an idea of what they are aiming at for medicine etc.
You can give them all the careers advice you want, but it won't always be taken. My ds is currently doing an MA; but we have wildly differing views on what he should do thereafter, and what will be available jobs wise.