Chicago and Duke are both private, but don't have pedigrees going by the list above.
There are lots of other factors. The ivies and public ivies (Mich, UCLA, Cal) have the best reputations and usually "good" urban locations. For instance, NYU and Cal appeal to people in their early 20's w/out kids and big COL concerns. The rest are regional schools, with the exception of Chicago and Duke, which are in the south side and south respectively. You can argue until you are blue in the face, but people from tend not to move to the south and midwest. Recruitment reflects regionalism. Chicago has a shaky reputation in recent years, which also damages its recruitment.
It's a private/public split.
Pedigree also doesn't help get those students placed.