The BLS and US CPI moved toward the current system for valid 'technical' reasons because the previous way was agreed upon to be bad:

* https://www.bls.gov/opub/mlr/1982/06/art2full.pdf

There is no internationally agreed upon method for housing/shelter, with pros and cons for each:

> International statistical agencies have unanimously adopted the net acquisition approach for durables, but there is no consensus about the best approach to the treatment of OA in the CPI16 (Table 1). Rental equivalence is the most popular approach among countries belonging to the Organisation for Economic Co- operation and Development.17 Johnson’s (2015) recent review of the U.K. CPI proposes using CPIH, which includes the costs of OA and is based on a rental- equivalence approach, as the U.K.’s main measure of inflation. Several countries in the European Union have refrained from incorporating OA into their CPI, although Eurostat is currently conducting a pilot study for the euro area based on the net acquisition approach. Australia and New Zealand use a net acquisition approach, while Sweden and Finland—like Canada—are using a partial user-cost approach. No country has adopted a full-fledged user-cost approach.

* https://www.bankofcanada.ca/wp-content/uploads/2015/11/boc-r...

In the Canadian CPI paper there is some explanation towards the complexities of shelter / owner accommodation:

* https://www150.statcan.gc.ca/n1/pub/62-553-x/2019001/chap-10...

* https://www150.statcan.gc.ca/n1/pub/62f0014m/62f0014m2017001...

People also often confuse the price of the asset (e.g., land) with the price of the home/structure.

> The [US] BLS views housing as a mostly “investment” item as opposed to a consumption item. So, for instance, when you consume a hot dog and have to replace it then the cost of replacement is a direct reflection on your well-being. A $1 hot dog that costs $2 one year later is a material change in living standards, all else equal, since the hot dog is an asset that you literally consume. A house is much more complex. [...]

> Of course, anyone who owns a house knows that it’s not that simple. You do basically consume your house over time. For instance, my home has appreciated substantially since I purchased it just 5 years ago and underwent a hellish remodel. At that time the cost of replacement was roughly $300 per square foot. But in the ensuing years the cost of replacement has increased to $400 per square foot. As my physical home falls apart over the years I will need to replace it. But the key point is that, as I replace these components the housing market is likely to revalue the total home value to account for this investment. So even though I am consuming my house over time I am very likely to recoup those costs.

* https://www.pragcap.com/should-house-prices-be-in-the-cpi/

It is a common mistake, for example with this story entitled "This tiny Toronto house is now listed for $1 million":

* https://www.blogto.com/real-estate-toronto/2020/07/tiny-toro...

The house (home) is not being sold for one million dollars. The land is being sold for $950K, and the buyer is getting $50K worth of structure.

Similarly if you are a home owner your home/structure depreciates over time so you have to do maintenance on it over time. And because of various shortages (e.g., lumber, plumbing fixtures) the cost of upkeep has gone up. Upkeep is a part of the CPI: the "C" in CPI stands for consumer.

And why the component is called Shelter and not Housing, at least in Canada:

* https://www150.statcan.gc.ca/n1/pub/62f0014m/62f0014m2017001...

It includes:

* Rent, tenants' insurance, tenants' maitenance

* Mortgage interest cost

* Property taxes

* Homeowners' insurance, maintenance, etc.

* Utilities: water, power, natgas

The consumable portions are housing/shelter are taken into account.