No they are 'forced' to buy a home.
The home that fulfills their needs is 1M. If they could find a home that fulfilled their needs for $5 and 10c they would spend $5.10 on their home.
The 'poor' person who sold their house to them in the poor area for $1mil ('where back in my day a house cost nothing') now has $1mil. The 'rich' person has a mortgage.