Wouldn't work, because most of those we classify as ‘elites’ wouldn't be smart enough to maintain a robotic society.
Not an issue that they would overlook. If this type of thing was actually attempted, then they would inoculate enough service personnel in every area of expertise to train and continue operations after the culling. They would only need to reset population to a manageable size, say 5-10 million, and then guide population growth as they see fit.
I have run into more than a few “elite” types that could not for the life of them figure out how to turn on a laptop.