The weighting applied to housing, healthcare, and tuition appears to be nonsensically low compared to the fraction of income most people spend on them.

Though to be fair CPI is computed nationally and things like housing prices are so localized that it's impossible to come up with a number that makes sense across the whole country anyway.

> CPI is computed nationally

There are CPIs calculated for each metropolitan area. When I'm considering my savings, for instance, I look at New York-Newark-Jersey City, NY-NJ-PA [1] and New York-Newark-Jersey City [2] statistics.

National CPI is useful if you're planning policy. Local CPI is better for individual planning.

[1] https://fred.stlouisfed.org/series/CUURA101SA0

[2] https://www.bls.gov/regions/new-york-new-jersey/news-release...

It includes rental, not purchasing homes

> It includes rental, not purchasing homes

Home prices work their way in through owner-imputed rent, i.e. the rent offset by owning the home. Home purchases include a utilitarian portion (the housing) and a speculative portion (the investment gains). We don’t include the stock market in inflation; we similarly don’t include housing prices beyond the housing utility. Nobody has to purchase a home; everyone needs a place to live.

Every study that tries to include housing prices finds an inflation figure lower than CPI [1].

[1] https://seekingalpha.com/article/4173463-cpi-housing-prices

the issue is that in aggregate, this is true, but its a case of Simpsons paradox. Housing price growth in cities exceeds CPI by a large margin, and has pretty consistently since the early aughts. Housing price growth in exurban and rural areas has largely stagnated since 2009. You get a strange issue where the people in top 25 cities are paid well and struggling to pay rent, and people in the bottom 20% of census tracts are paid very poorly if at all, and are also struggling to make rent. Slicing even further, there is a generational component, where young people moving to a new city or out of their house within the same city generally pay more for rents than someone in the older generation for a number of reasons that can basically be summed up as "the small land lord rental market is inefficient and YoY rent growth after occupancy historically has lagged market rate rent growth for people moving in to a vacant unit"

This is correct. To expound on this, bay area housing is very expensive vs rent because the market believes that the price of housing will appreciate. In other markets the cost of owning is nearly flat with renting after factoring in the down payment. In those markets, the market of buyers believes that housing will not appreciate to the same level.

You cannot include for sale housing in the index because the price paid is a speculation/estimate by the buyer (future looking)

Rent is a snapshot of today's price.

It doesn’t work in practice: the rental supply mostly consists of condos, or college housing. There are few “three bedroom two baths with a one car garage” in good shape.