One day banks will accept Bitcoin as medium of exchange and accept deposits from bitcoiners. As soon as the world powers accept it as medium of exchange.
Why would you want to send your Bitcoin to a bank when Bitcoin was literally created to work without banks and third parties? 
Even if they start accepting Bitcoin they would not allow you to withdraw whenever you want, they would charge additional fees, they would force you to use their ''approved'' wallet, and other crap like that.
And they would probably turn your BTC that you put in them to fiat back while doing operations - so, yeah.. It dissolves the logic of why BTC appeared in the first place.