Largely I do not see banks survive in a Bitcoin world.
Banks do two things:
1. Store large amounts of money securely.
2. Transfer money.
Banks do not only do those two things, you left off the most important thing and that is banks are businesses out to make as much profit as possible and they have a legal licence to print money as well, beat that. They will catch any runt that tries to take their stash away and put a gun to their head. Bukka! Over innit.