I think the main issue I see with your note about the difference in home prices is that you could stretch that out to say 1915 and 1950, and you’d be hard pressed to explain that economic growth was fake or don’t occur. Even in your example, the economy didn’t grow 6x, but how has resource utilization changed or supply and demand globally? I think a further analysis will show many factors going into that home price, and some of those very much are just simple economic growth and/or supply and demand of materials.
As always it’s also the location. Look at home prices in, idk, Toledo, Ohio. How have those fared in your same time period?
After all, it's really cheap estate and lots of reserve labor...
Ah right, and here we come to the critical issue which is horizontal integration. Even shipping to Toledo is going to be more expensive, not to mention availability of variety of things.
Then you get to deal with the interesting "small town culture" vibe, and lack of educational options.
Certain categories of the CPI have experienced extreme inflation over the last 16 years, this gets reflected in the wages of the economically mobile and in turn raises the GDP - however we don't really price housing into the CPI in a sensible manner, and due to USD dominated trade - imports and products which compete with imports don't inflate.
The discrepancy between PPP and nominal (USD) GDP seem to be telling a story.