"Elite" means "the best" ("the selected") - not the ironical take you have assumed. Here, the point is whether those who take the slots that should be reserved to an elite proper actually are elite proper. While many get said slots from "wealth and social standing", others get them from non-exportable (non-indicative in administrative jobs) success in business and political communication (the ability to get elected does not indicate a best candidate for administration).
The poll of those who will take them slots is larger than those of the "wealth and social standing". So, the strategy to get some "educated elite" is larger. And the concern includes both the quality of education and its distribution.
> universities
We have to act already before the primary school level, as the societies I know show.