Except, in fact, it actually is how they do the rent portion of CPI. (Well, its not city rent averages, they do same-unit rent changes and average those.)
> It currently uses a metric called "owner's equivalent rent".
No, OER is used for...OER. Rent is used for rent. They are two separate subcomponents of the housing component of CPI.
More complete description:
https://www.bls.gov/cpi/factsheets/owners-equivalent-rent-an...