Why would inflation push people into banks? In my (EU) country, banks don’t offer anything that matches current inflation besides speculative investments.
In USA at banks near me, I don't find high liquidity with decent returns. Rates on savings accounts are paltry, and CDs are only liquid if ignoring early withdraw penalties.
I use bank to accept revenue and transfer it to brokerage houses where it sits in highly liquid money market with better returns than bank savings.