Banks are not into existing cryptocurrencies that is for sure. Banks are the number one enemy of decentralized currency why would they adopt it? and talking the volatility of cryptocurrencies, banks having an uncertain edge will never be in place. New stable coins will be created for them, a well regulated and backed coins.
Why would the banking system consider the decentralized currency an enemy,they will be getting business from exchanges because if you want to purchase these currency you need the help of the banking system to send money and that means the banking system will get business and all they will be looking forward is business and if there is a clear regulation by a government then i bet the banking sector will not have any issue dealing with the crypto exchange.