Most people HAVE NO BITCOIN. Most people do have collateral. A bank is able to judge the credit worthiness of people with collateral and loan them bitcoin. It would be a way to buy a house and have a mortgage denominated in bitcoin.
The value of banks is this ability to judge credit worthiness and give people who have no bitcoin access to bitcoin. The banks are willing to assume the risk. They are willing to pay interest to people who trust them and deposit bitcoin in banks
Obviously, you failed to account for something
Something which will render the whole idea of lending bitcoins unrealistic as of now. And it is not Bitcoin depreciation like what you mean with fiat that will make this idea fail. It is the exact opposite of that. I mean possible Bitcoin appreciation. i.e. its price rising. Let's assume a bank offers Bitcoin deposits at 1% and loans bitcoins at 5% interest rates annually. Now it takes collateral at, say, 120% dollar worth of the current Bitcoin price. Someone takes a loan from the bank and provides real collateral (let it be his house). Then Bitcoin price surges a few times within a year, and the borrower happily defaults on his loan buying a better house instead of his collateralized one and still having some bitcoins left in his pockets. But the bank can sell the house only for a part of the bitcoins it loaned out while it still has to pay interest on Bitcoin deposits it attracted, right? And from where will it get the bitcoins outstanding?