One day banks will accept Bitcoin as medium of exchange and accept deposits from bitcoiners. As soon as the world powers accept it as medium of exchange.
How is that going to function? Would it be that banks will accept Bitcoin from customers, convert it ti fait using their own rate and then deposit fiat to customers account or how? Why would someone even want to go and deposit their Bitcoin in the bank when they can bear the security of their coins by themselves? Any time these ideas of Bitcoin and banks comes up, I always ask my self so rhetorical questions and it is even pointless to think that there should be a Bitcoin bank meanwhile the Bitcoin itself was developed to avoid third parties from interfering into your transaction.