In future, when bitcoin will dominate in sending - receiving - depositing funds kind of bank works, I believe banks will start different type of banking like providing safe vault or mortgage kind of services alone. Banks will fall.
I don't think the banks will fall either just because of bitcoin. Remember who is with banks and that is the supreme government of a country. And I don't think that government is going to allow it for banks are really important in a cycle of an economy of a country but I think that bitcoin will be considered by government too.
Exactly, banks have support from the governments and even from the people as it is the strongest financial institution we have which is running since long time and the fact is that people have blind trust on it.