Accommodation costs are the first part of any sensible measure of inflation. If you're not factoring in housing then you're fudging the figures.
Yes? Who says otherwise?
As long as accommodation isn't 100% of your basket of goods and services you use to measure inflation, accommodation can rise in price faster (or slower) than the basket. This ain't exactly rocket science.
Many people don’t see housing inflation - if you bought a house in 2020 and house prices were up 80% since then it doesn’t affect your housing costs, especially in the US where mortgage rates are fixed for length of term even if interest rates sky rocket.