Got data on this? In my anecdotal experience price per square foot has shot up in urban places, which is where the jobs for young people tend to be concentrated.
Maybe true in aggregate, but not true of many cities these days. For example, you can't touch a new home of any size in the Bay Area for less than about 750k, and that's even a long stretch. 250k for 2,000sqft would be a dream for many here.
It looks like they applied CPI directly to the cost of housing. That is not correct.
CPI has a component of "owner's equivalent rent", which should be removed before cost-correcting the price of housing. Otherwise, you are removing the increase of the item you are searching for an increase of (Housing accounts for 1/3 of the CPI correction.) Their graph is instead showing that the buying power of a dollar is roughly constant when 1/3 of the CPI basket-of-goods is corrected with CPI.
Calculated Risk has a more sane analysis, you will note that the graphs are corrected with "CPI less Shelter": http://www.calculatedriskblog.com/2016/11/real-prices-and-pr... He doesn't include price/sqft, but note that there is a 44% increase in real prices between the 90s and now. Square footage has not gone up by that much in 20 years.
As a side note: AEI is a fairly political org, I wouldn't rely on their accuracy for anything involving stats, or math in general.
However this is only new homes, not used homes.
http://www.aei.org/publication/todays-new-homes-are-1000-squ...