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 you're free to choose to use bitcoin wallet or bank bitcoin. both have the same function that is a medium for storing bitcoin, the difference is that you can make a profit when you save your bitcoin in a bank bitcoin just saying.