Falling asset prices are a huge roadblock to inflation. With the decline in stocks/ crypto people will put many new purchase on hold. I would not be surprised to see inflation moderate significantly in 2022 and thus it will not be as urgent for FED to raise rates, although their will likely be a few necessary rate increases in 2022 and 2023 regardless.
The FED new goal is to ensure homes and autos can remain affordable to most Americans.
Asset prices factor into it, but inflation has a lot of inputs.
And inflation in different goods can move in different directions.
Higher housing costs are an outcome of large-scale internal migration decisions. These can take longer to reverse than food costs, which largely boil down to transport issues, or consumer goods costs, which are an outcome of COVID-related demand whiplashes.
Stocks, crypto, food costs and consumer goods could all go down next year while housing prices keep going up.