> To arbitrarily exclude the biggest expense to consumers from CPI is pretty misleading.

Why is there so much misinformation about the CPI? Literally the biggest component of the US CPI (at 33%) is housing/shelter. See Table 1, column Relative Importance: https://www.bls.gov/news.release/archives/cpi_02102021.htm

At least get familiar with the definition before criticising anything.