It cant because old people and big fortunes are stored at banks, soo it wont happen at all, as some people said in the past save your money at the banks and enjoy the fees they pay to you, since they lend your money to others. Even the p2p transactions does requires bank, without them bitcoin would be dead since we need to transfer money between accounts. Bitcoin wont replace anything, it can improve all services as remitances, providing a fair system and not abusive charge due to cambio.
People who put their money to banks just want to be safe with their money, but actually they have a business where they get the money they save.
Bank is just good for saving but not for investing, however there are also some who what to fully hide their real wealth and they can store their money into bitcoins but I think there are only few of them compared to the total number of banks depositors.
Yes people use banks for saving to their business so that they saved money for their future. Banks is the popular saving place in our society but when the others seek bitcoin and spread it maybe the bitcoin become the popular saving place also and investment place for everyone.