Common folks are parties to Supreme Court cases-- Ernesto Miranda was no elite-- but, by and large, the lawyers who argue before the Supreme Court are an elite among the elite. I have practiced law for 30 years, and argued dozens of appeals before many federal and state courts of appeals, and I have never argued a case in the Supreme Court and will in all likelihood never get to do so.
So somehow or other, a common folk type of person must have access to the bigshot lawyers. Sounds pretty hopeless unless one has the type of case that the ACLU likes.