Class Diversity on the Courts?

Orin Kerr, with a lot of tongue-in-cheek, had this to say (among a few other things) about the President's current shortlist concerning potential nominees to fill the vacancy on the U.S. Supreme Court:

No matter who he chooses, Obama will continue to break new ground, or at least help bolster some of the low numbers of people of certain arguably underrepresented backgrounds on the current Court. For example, Elena Kagan would become only the second former Harvard professor presently on the Court (joining Justice Breyer). Either Kagan or Wood would be only the second Chicago professor (joining Justice Scalia)...

[...]

....Elena Kagan would also bring notable educational diversity to the Court. Kagan would be the very first Justice ever to have attended Princeton and then Harvard Law. Obviously, that would be a major break after two consecutive nominees who had attended Princeton and then Yale Law (Justices Alito and Sotomayor). Whoever Obama picks, I think it’s clear that Obama faces a major choice and that his selection will be a historic occasion.

Now, when we talk about "diversity" on courts, we often, as my fellow bloggers on here, mean gender, ethnic, or cultural diversity.  And Kerr is obviously playing around a bit here with those norms.  But maybe there is a serious point here too, one concerning class and socio-economic background. While not always the case (ie: Judge Sotomayor's fascinating working class background), given the cost of attending and the preparation needed for admission, often those candidates who attended Ivy League colleges and law schools may come from wealthier families and thus are representative of a certain socio-economic class. So: is there a need for this kind of diversity too, members from a broad spectrum of socio-economic background?  Wouldn't coming from a working class background potentially influence a judge's views on anything from labour laws to the importance of equal access to public services?