We are only just seeing the beginning of widespread inter-chain trading without exchanges. Eventually it won't matter which token you have in your wallet, compared to what the vendor wants to be paid, it will be possible for it to be converted on-the-fly anyway.
Banks are extremely conservative by nature, and electronic transfer is something that they still mostly rely on 30-40 year old technology - most POS terminals still connect to the bank over analog modems through the PSTN.
They are stomping around in the government lobbies trying to impede the progress of cryptocurrencies, but it's like the competition between dinosaurs and burrowing mammals just after the comet struck. They don't have a chance, but they aren't gonna publicly admit that. Almost all the big financial and holding companies are putting significant investment into finding ways to make use of the technology but they are held back by ideology and, secretly, by the fact that they are being steamrolled over, one bit at a time.
Pretty much any city over 50,000 population now has a cryptocurrency trader converting to fiat. Give it another 5 years and every change bureau will be trading them too, some are starting to dip their toes in it.
But as with all technologies, the biggest spoils will ultimately go to those who effectively adopted it early and that's us :D