On an inflation adjusted dollars-per-square-foot basis, housing is exactly the same price as it was in the 1970s [1] -- right around $115/sqft in constant dollars. 2008 didn't actually make a big dent on average.
The reason houses are more expensive today than they were in the past is that they're on average twice as big. This is due to city zoning ordinances, not inflation.
Similarly house prices exploded in major metros like SF because of artificial supply constraints. The city won't allow new building -> refuses to allow smaller units -> prices go up. Again, not inflation.
[1] https://fee.org/articles/new-homes-today-have-twice-the-squa...
I think that is the reason CPI hasn't increased. CPI only accounts for rent and not the cost of actually buying the house. There are definitely highly inflated price to rent ratios particularly in land constrained urban areas.
I think a better way to put it is that there is low/no Consumer Price Inflation but there is tremendous Asset Inflation (in stuff that wealthy people buy).
And perhaps if there did need to be inflation, then perhaps this is better than the reverse (i.e. high CPI inflation which would impact people's ability to buy the basics)?
The point I was making was that the price of housing on average ($/sqft) is the same as it has always been. Since we know major metros have gone up it likely means that tier-2 and below cities have actually gone down.
Further, it might be nuanced, but major urban areas aren't land-constrained. They are constrained by their city councils staunch refusal to permit new, tall construction to the benefit of existing landowners and at the detriment of renters. This is not an inflation-linked issue however but a city policy issue. It's strictly supply and demand.