I mean, generally speaking in our fiat system housing prices go up so that houses keep their value (if prices didn’t rise with inflation, then houses would loose value over time).

The reason why we see housing prices not coming down right now (if I had to take a guess) is high interest rates. Since a lot of buyers have locked in low interest rates the sale price for existing homeowners must offset the new interest rates, otherwise they’ll loose money on the sale.

This would be true in a hard money standard too, as even if the prices of the houses remained constant, higher interest rates would make mortgage payments higher (thus increasing the true cost of the house). So existing home owners would increase prices to offset higher interest rates.