Yes, and those cities also presumably don't have the problem of segregated neighbourhoods. (also those cities don't tend to occur in my Old Country, but perhaps they've made progress there since I've been gone? Protip: never attempt to live in a "city" which is younger than you are. Survivre plutôt que vivre)

All I was claiming is that the elevator is necessary but not sufficient: monocultural neighbourhoods were much less likely to arise back when number of flights of stairs put a significant natural gradient on the price point of each buildable unit.