Banks would not disappear. Maybe the way banking works might become different, but even that is a remote possibility.
It's already changing. If I compare the banking experience right now, with how it was years ago, then it has been changing a lot (for the positive). For the first time in years the customers are being the central point of attention, and not the banks with their greedy intentions. It has either be an effect of them feeling pressure of alternative payment forms such as Bitcoin, or because people were taking distance from banks more and more. Something has sparked this effect.
What you need to remember is that banking is big business. If bitcoin were to cause the banking industry problems, the banks would fight against bitcoin. And they would wage that war through government; By using legislation to keep bitcoin from causing problems to their industry. And government would happily play along.
If Bitcoin forms a threat at the time it grows too large, the government won't let it come anywhere near the edge that it is harming their economy and banking system. Every action will be taken to push back Bitcoin. That's why I am perfectly fine with how Bitcoin is right now. I don't even want it to form a threat to the current system. I prefer to have everything stay as is the case right now. People are happy, so why do we want it to replace all kinds of institutions and currencies? There is no need for that when Bitcoin can work alongside all that without any problems.