Thanks for your comment. You raise a good point about CPI inflation, namely whether it is an accurate measure of the price increases households face.
One of the issues is the (fairly) constant weights. In reality, when price changes are heterogeneous across goods, people substitute toward those getting relatively cheaper. This is better captured by PCE inflation - which is also the primary measure used by the FOMC (Federal Open Market Committee) responsible for monetary policy conduct.
PCE inflation is lower than CPI inflation. The latter is used to adjust social security benefits etc., meaning they get corrected for a higher inflation rate than the one many economists think is the most appropriate measure.
Rising costs of housing and asset inflation are two factors policymakers should definetely have on their mind. The expansionary fiscal policy and the low interest rates contribute to these factors. There may be need for some distributional policy adjustsments to ensure part of the population isn't harmed.
Thanks for bringing some nuance,