What sets Bitcoin apart from any other form of finance is how the individual user can fully control ownership of their coins at all times. Albeit one might raise the point funds kept in a bank account is in the control of users as well, that is certainly not the case. Consumers can send money to other accounts and withdraw money from the ATM, but they still have to go through the bank before gaining access to the money.
http://fintechist.com/take-full-control-finances-bitcoin/True. But it might be a convenience users are willing to give up.
If Bitcoin banks are set up and manage to gain the confidence of the public, people will be willing to give their bitcoins to the bank in exchange for interest payment.