You’re not missing anything. Housing is included in CPI as rent. Housing purchase prices aren’t included because they represent both current and future housing consumption (people don’t consume a house within a year).

Don't rent and housing purchase prices follow each other, roughly ?

Nope. They can go inverse when, say, an economy collapses and everyone is forced out of their homes as they go underwater on their mortgages and but they still need somewhere to live. Kind of like 2008/09

> an economy collapses and everyone is forced out of their homes as they go underwater on their mortgages

People are not forced out of their homes when their mortgages go underwater, they're forced out when they can't afford to pay the mortgage (underwater or not).

or if the bank calls in the note because the asset/collateral becomes devalued.

Housing_price = rent * reciprocal_of_interest_rate

You’re not missing anything. You just decided to look up the actual answer rather than just guessing what it was.

Problem is that outsourcing and automation has collapsed the cost of most non-essential manufactured goods. These artificially depress the CPI and hide the crazy inflation that is occurring in essential areas like housing, health care, and education... basically in anything that can’t be outsourced or automated.

Massively aggregated statistics like the CPI border on bullshit. They have too many hidden variables and gloss over far too much detail.