What’s happening with housing is the opposite of shrinkflation. There’s always been more or less desirable neighborhoods. When you see prices skyrocketing in a particular neighborhood, it’s because that neighborhood is moving up market. But house prices across the country as a whole aren’t going up. It’s just that Mountain View has become what Scarsdale used to be, and the current version of Mountain View—a boring nowhere suburb with housing prices to match—is somewhere in the Kansas City or Dallas suburbs.
Including X & Y may greatly skew the results higher or lower, but if the percentage of people purchasing X & Y are low, then they don't have much impact.
The CPI methodology isn't great, but it also isn't bad. Removing volatile sectors makes sense when trying to identify trends, but it doesn't make sense when those volatile sectors are a large component of consumer spend.
Since most of the data used by the CPI calculator is publicly available, it is possible for people to construct their own CPI metric and track it over time. This is helpful if you want to get an accurate indicator of the inflation you've experienced over time, or if you're wanting to push the narrative of higher/lower inflation over a period of time.
It’s bad for any discussion involving wages since your earnings need to go up by more than CPI to tread water, in popular areas.
At a personal level, the CPI really isn't set up for cities. It is simply not considered in the CPI that housing would be such a big cost that would outweigh anything else. The "why" seems to be speculated by another poster, though I can't speak to that as I'm not deep enough into economics.
The opposite, people are in significantly larger and better equipped houses than they used to be.
I also think 20% is pretty steep outside of the most desirable areas in the US, which are akin to complaining about the pricing becoming unreasonable in your country club. The top end of the market shouldn't be used to track inflation, we should use the median.
Even if you did include it, the numbers wouldn't change. For every Seattle or Denver experiencing heavy growth in the housing markets, there's a dozen Lafayettes experiencing slow/no growth.