Spet0789 wrote: It's a fundamental misunderstanding of how banking works.
It isn't. What you are suggesting is a fundamental misunderstanding of how banking works on an aggregate basis. Banks don't offer deposit accounts for the good of their health. They'd rather not bother and would just use a wholesale overdraft at the central bank if one was on offer.
They offer retail accounts because they are essentially required to by banking regulations, as Parliament, via the central bank, wants a working payment system in Sterling - and has settled on the outsourced model.
How could a bank pay any interest if depositors were "holders of cash that is notionally stored in a bank"? That would be economically equivalent to just hiring a safe deposit box and jamming it with £50 notes.
Loans create deposits. Banks earn on the differential between those two. They offer interest largely to stop cheap depositors leaking to National Savings and cash which would leave the loan book exposed if enough of it disappeared.
When you put the £50 note into a bank that causes an automatic loan to the central bank remunerated at the base rate (that's what banks reserves are) and a corresponding deposit in the bank.
It is a matter of public policy to allow depositors with interest. The central bank could easily dispense with that by offering unlimited 0% overdrafts to those on the Sterling framework. The banks wouldn't need to attract depositors away from cash and National Savings to balance their loan books and the price would drop to zero.
In fact banks would probably start charging again to process your payments. And the way base rates are going at the moment we might start to see that happen anyway.