It might also be that the central banks are printing money like hell, and people look for places where their value stays better.
For example ECB (european central bank) is issuing 60 billion euros new money each month, and buying bonds with it. That is half of the bitcoin market cap.
CPI is fairly useless anyway. It ignores where the huge money displacements are actually going: hint, not bread and circuses. The money the ECB is displacing is institutional investors money and causes inflation in things like housing, stock markets, VC funds, and yeah, probably cryptocurrency.
Rent is included in the CPI, and it usually co-moves with housing prices .. and yet .. it means no difference: https://www.ecb.europa.eu/pub/pdf/other/mb201008_focus06.en.... (it's much more drastic in the US CPI - probably because more people own their homes in the EU and gentrification and other effects are a lot slower too? who knows..)
For example ECB (european central bank) is issuing 60 billion euros new money each month, and buying bonds with it. That is half of the bitcoin market cap.