It's very unlikely that banks would accept btc now. As far as I know, banks likes to keep it stable and static unlike if they were to incorporate bitcoin which is very dynamic. However, there's a chance that they may accept it in the future; I think they are in the process of figuring out how to make use of it properly.
Bank will always live on what they believe, they make everything centralized because they want us to trust them and bitcoin is just a big competition
to them so why would they accommodate it. Bank only accept legal tender or legal currency, bitcoin is not considered as legal currency by the bank.