I doubt that will be the case at least in our current time, I think bitcoin can change the way money and economy works but banks are an established part of it, I think it would be more reasonable for bitcoin "banks" to appear sometime in the future when bitcoin is more mainstream.
Let's say Bitcoin does very well, and manages to reach 1% of the world population to adopt Bitcoin at some point, then still there are the other 99% where banks play a very important role in their life. Bitcoin won't even make a dent in the bank's way of doing business and how they exist. People must forget about that.