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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.
I do think that for banks to start accepting bitcoin for deposits and for payments, would mean that the government of the country in which such bank operates, must have acknowledged it as an accepted currency and trade it internationally. Else, banks have no right to accept what the government hasn't accepted yet, officially.
I think that many individuals even in countries where Bitcoin isn't yet a legal currency, already own bitcoin and maybe other cryptocurrency investments too and it is just a matter of time before more countries accept it, because the idea of cryptocurrency is that which supports an individual to own it and transact with it from any part of the world, as long there's access to internet and mobile devices available.
The world is evolving both technologically with advancement in artificial intelligence and digital currency. We even see robots taking over human jobs just because those that fail to adapt to the times get left behind. Thus, I think it is just a matter of time for banks in both major and minor countries of the world to transact, accept and even exchange crypto currency on the internation, market.