Housing prices are long term "bound" by CPI, not the other way around. More specifically they have always mean reverted to CPI if you look few hundred years back. Robert Shiller wrote a lot on this topic.

Also, the current level of divergence between housing prices and CPI is nothing out of the ordinary. It will correct itself over time (either houses will become cheap or CPI will catch up).

If you want a simple explanation as to why it is that CPI bounds houses and not the other way around - just look at the recent post-covid deurbanization trend (and the carnage that's going on in San Francisco or New York real estate markets). There's so much land that can be utilised once you understand that you really don't have to be in downtown New York. Then, homebuilding costs are basically CPI.