And some jobs do. As I've noted elsewhere if you want to go into Big Law, you go to a relative handful of law schools, which are heavily fed by undergrad Ivies, and clerk at a high federal level.
Yes, like I said before, this hasn't de-stratified the job market. Jobs that want to select applicants by class can find plenty of ways to do so easily
E.G.: More expensive vocational programs that haven't been subsidized, selecting among universities for especially "prestigious" (read "class-signaling") ones, baking cultural assumptions of the upper classes into the expectations surrounding "professionalism" in the interview process, etc
