“Probably there was a fundamental reason for the price increase: larger houses, rising incomes, greater productivity, introduction of loan program which raised demand and allowed more homeownership, etc. ”
My Theory : #1 The rise of women in the workforce during WWII and subsequent increase in dual income families in the following decades.
Without any stats or back-up I believe this to be the primary cause of the large post-war shift upward in the home prices per the Shiller chart, resulting in a new higher plateau from post WWII to 2000.
Rates are secondary.