Actually, for a fact it is right that the transaction fees for overseas transfers is very minimal if we use bitcoin for these transactions. Bitcoin is even more faster for such transactions. But people still use only those traditional methods of transactions. Because they find it ore convenient. It is their prudence, that does not allow them to shift to better methods of transfer. Actually people have natural tendency to resist change and that is the main problem that is not letting full bitcoin adoption.
The only thing in here is that Bitcoin is very volatile and its price/value isn't stable and this is a big "NO" when it comes to banking but if Bitcoin is not volatile it will be absolutely adopted by every bank in the world. We can't do anything with the volatility part of Bitcoin because its main feature is being a decentralized crypto currency the no one controls neither a government or a central bank and this gives freedom to every user of this technology. Maybe banks will not accept or adopt Bitcoin but there is a high chance that they will surely adopt the blockchain technology of Bitcoin because they already know what this technology can do and the efficiency they'll get when they use this innovation.
When it comes to transaction efficiency, Bitcoin is surely more efficient than bank transaction because of the time and energy that a person can save with this method and there is no doubt about that.

I don't believe that banks will accept crypto currencies but who knows anything might happen in the future and there could be some change of heart that will occur.
