Your assumption is flawed because home prices don’t track core or headline inflation but rather income inflation and incomes have declined 4% in the last 5 years, probably a big part due to Global Wage arbitrage. Headline inflation actually depresses home prices.
This makes sense, for instance say inflation is at 15% a year but your income is increasing at 2% a year. Now the price of goods is skyrocketing..groceries, oil, transporation, insurance etc. In this scenario your net affordability each year for housing is decreasing because more of your budget is being eaten up by the rising costs of goods and services.
So you can’t calculate prices of homes based on inflation. It’s income growth that is KEY. In the 90s income growth would have been approximately equal to inflation or slightly more but in the last 5-7 yrs income growth has lagged inflation. The difference has been picked up by credit spending but that is no more so we’re in for some interesting times ahead.
To give you an example, in my line of work, which is IT consulting, they are paying the same hourly rates they were paying in 2000. In some cases rates have gone down due to the huge influx of cheap H1B labor and especially L1 labor which bypasses the caps and are paid peanuts.