No it won't even though will completely use bitcoin it won't make banks disappear because banks are important for a society and the government is going to rely or completely force the people to keep on using banks. You know, government can control everything but not bitcoin so still they will not let bitcoin make banks disappear for they are earning great there.
Yes banks is heavily funded and government backed institution, so it is impossible for bitcoin to make bank disappear. Aside from that bank services are well established and people gives high regard to whatever their bank suggested to them because of the trust level that is already established. People that care less to financial system would more likely obey what their bank suggest them to do rather than hearing an anonymous person and be persuaded to accept bitcoin and trash the banking system in their lives.