Even if the crypto currency is fully legalized throughout the world, the banking system will continue to exist. Banks have a lot of their specific functions, in addition, they serve the financial side of the state. Therefore, banks will exist as long as there are states.
Banks will really continue to exist in the world even if the cryptocurrencies are legalized. As you have said they have their specific functions the reason it will really exist maybe forever.
What will only happen to the banks are improvement and development. Since cryptocurrencies might be legalized in countries, they will find a way to develop their securities and their services for that.
This could not affect banks if cryptocurrency will become popular in the world. First bank is a big industries which most of all people used it and store their money in there.