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 do nothing about competency and decentralization so they maybe forced to do this "if we can't beat them join them" thing. It seems banks are just another option when it comes to engaging financially because some countries are now eyeing Bitcoin as something like a strategic reserve so maybe we can see banks will soon show it's interest on investing or maybe integrating Bitcoin into their financial capability to offer services for their clients.
You need to know that most of the strategic reserves of countries like the US, EU, Russia are bought and held by central banks, the government has no authority on this matter. So which country is looking to add bitcoin to its strategic reserves, that is the intention of the Congress and the central bank. So whether we see bitcoin reserves soon, or whether banks adopt and accept bitcoin deposits, depends entirely on the central bank's decision. Don't think the president, the treasury department or any agency has the power to do that.