Fermion
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The OP assumes that everyone needs a house, which is nonsense
Ding ding ding, winner!
When retired on a fairly big budget, what are you mostly doing? Traveling. Why do you need a 3 or 4bd big expensive house while vacationing in Costa Rica or Europe?
A retired couple could likely drop expenses by $10,000 to $15,000 a year by significantly downsizing or even selling their home and renting a tiny 1bd apartment. Just the saving on insurance and taxes for a lot of people would be more than the rent. The money tied up in the house could then be invested to generate positive real returns.