I do not think that will happen anytime soon. In the current world economy, banks are the foundation of money in general, and when I say money in general I refer to fiat money. But the things, of course, can change a lot with time...
Well it is not going to happen either because banks are really stable for a long time for almost centuries. They are already in the economy and they are contributing big part for the wealth of the country. So if bitcoin is going to make the banks disappear then that is going to be a big loss for a government but I don't think banks are able to make bitcoin disappear too.
The bitcoin will not make the banks disappear. The banks can use the bitcoin instead of the fiat, and reduce running cost.