Since i believe that fiat as we know it is not going to go away in the future, i have to say banks which are working with cash/fiat are not going to disappear either. even if bitcoin becomes big and adopted by all the people in the world , cash is still going to be around. so banks will be around too.
Yes banks are going to remain always there because the people are depending into fiat / cash money. And they are going to have hard time to adopt bitcoin especially those people who are into depressed areas. Still they are going to trust banks rather than bitcoin as they are lack of knowledge about bitcoin.