I think we already have that... It's called "bank fees", i.e., depositors pay the bank to keep their money instead of the bank paying interest.
I'm not aware of any fees that are instituted "instead of the bank paying interest" unless you're talking about something like a low balance fee on a non-interest bearing checking account.
Edit: for example, https://www.bankofamerica.com/deposits/checking/personal-che...