Bitcoin the future of Banking is possible, but only if the governments and there specific financial body accepts it. But mostly they won't, as clearly many countries had already implemented regulations and many are coming with it, so it will be there with Banks in the future. Moreover many people are old school, and they won't rely completely on Bitcoins regarding transactions.
Banks might bring in Bitcoin in future, but completely making it the future of Banking might not be possible. But this will make banks think to increase there facilities with hassle free banking.
I totally agree with you. If all Governments, banks and financial corporations accept Bitcoin, it will be treated as a kind of money. But I don't think that it will replace cash completely.
If bitcoin replaces cash, then banks will have no reason to exist, so I don't think that will ever happen. If bitcoin succeeds, it will probably continue to be used as a store of value, just like gold, and as soon as stabilizes it will be used as a form of payment as well (I'm assuming that when BTC stabilizes all the scalability problems will already be solved). It will definitely be used for international money transfers, because even as it it, it's way better than the current options. It's faster, it has lower fees and it doesn't need to go through an middle man, so it's already great for that.
As soon as is gets better developed infrastructures, like crypto cards, or good mobile wallets, it will also be a great option for payments in undeveloped countries for the people that don't really have access to banks. Those are probably going to be the test pilots targets, for bitcoin as a payment method in the future.
Basically bitcoin will shine as an asset and it will probably force banks to evolve, because they now have some competition when it comes to (assets and currency), but it will never replace fiat, and that is not it's purpose.
