Not sure what the point is. Chase checking accounts pay for access to branches and other Chase products. If you want yield there are checking accounts that provide that. Though the correct move is to use currency correctly by using the transacting medium (cash and checking) separately from the store-of-value medium (money markets and Treasuries).
It’s easy to get savings account rates above the inflation rate right now and even well known national brands like capital one offer instant online accounts at 3.2% or higher.
"Passbook" is the traditional term for these accounts.