[spywaregorilla]

income cannot define social class by definition.

I would say its rather backwards. Thinking of things as lower class seeks to afford rent, middle class seeks to afford housing, and upper class is beyond it. House ownership is basically the cornerstone of class wealth in the US. Prehaps with secondary lower/middle/upper modifiers your degree of success there (e.g. upper middle class comfortably affords their house, but it's still the bulk of their wealth; lower lower cannot reliably afford rent)