The source If anyone is interested to read more:
http://www.cnbc.com/2017/06/26/barclays-bitcoin-regulators-fca.html
I sadly don't believe that the banking system will ever adopt bitcoin, If they start doing so, It would be for a particular reason they hide (most likely to eventually control bitcoin). The maximum that could happen right now is making bitcoin legal in some countries.
Large financial systems such as Barclay's will be very careful of applying bitcoin to their bank.
Because this is a big bet that can make them more interested customers or abandoned customers.
I think that a bank can surely adapt bitcoin normally and there are certain exchange with other currency then why can't bitcoin be part of it? well in our country I am using a wallet that are supported by a bank I can certainly withdraw my bitcoin and converting it with fiat in an ATM using a cardless transaction by providing me with a 16 digit number and a password to withdraw my bitcoin, I think they can work together in some other way a bank can surely profit with it.