I’ve always disliked this, but shocks to those markets keep them excluded.
But it's important to distinguish between a house and housing.
A house is a capital good that provides housing/shelter. So if the prices of houses got really expensive but rent stayed the same that wouldn't show up as inflation.
No, it doesn't. In the US, the US Bureau of Labor Statistics explicitly includes food and rent in it's CPI.
https://www.bls.gov/cpi/overview.htm
I’ve always disliked this, but shocks to those markets keep them excluded.