Your example was also fatally flawed because it buys into the notion that white collar work is not working class.

White collar laborers are labor; they are not capital.

I make a couple hundred thousand dollars per year. I have far more in common with a nurse or a teacher or a store clerk than I do with somebody who was born with $10MM in a trust fund, and who makes as much as I do (by selling my full-time labor) just by buying and holding VTI.