No because if there an bitcoin bank then how about our bitcoin wallets? that we use to stock our bitcoin from earnings and if there an bitcoin bank i will not totatly deposit my bitcoin if there an fee's like bitcoin wallet it much more better to use bitcoin wallets than bank 
just saying.
I think if bitcoin bank there though, they will not force you to use their facilities, they will not force you to leave your bitcoin wallet, you are free to choose a bank or bitcoin bitcoin wallet, it depends on their own comfortability just saying.