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.
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.
Some individuals don't want to take full responsibility for the safety of their funds. They usually want to transfer the custody of funds centralized platform. I have heard from people that they prefer keeping crypto in banks because they can't keep seed phrases safe. Others are used to the bondage of using banks that they detest freedom.
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.
Banks can act like exchanges if the law allows them to operate that way. The US is a pacesetter in the global financial system. Other nations might follow suit if the US government empowers banks to engage in Bitcoin transactions.