The direction of causality matters though. "Houses will become cheap" and "CPI will catch up" mean very different things for the average new family trying to afford a house. The first is cause for celebration; the second just means that instead of struggling to afford a home, they'll struggle to afford anything.

It wouldn't surprise me if the second is closer to the truth. Homebuying is close to where money is injected into the economy: when the Fed drops interest rates, mortgage rates drop, the home price you can afford for a given income goes up, and housing prices go up to compensate (particularly in land-constrained areas like Vancouver or the SF Bay). Other industries like food don't go up until that money has had a chance to circulate through the economy and make it to the average food buyer. I'd expect to see large increases in the CPI over the next decade, with housing last decade being a harbinger.