Not quite yet. Remember banks are more than just places for storing money, they give out loans to individuals and the government. Sure someone can always make a bank that uses only bitcoins but since people can store their bitcoins in their wallets anyway, there's less incentive in letting others handle one's bitcoin unless the interest is high enough.
That is why and it seems unlikely that cryptocurrency can replace old financial institutions, banks continue to innovate and banks continue to keep abreast of developments in the era that make them continue to be strong. Nothing can replace the currency in every country because it is part of the history of the country itself. Cryptocurrency does have advantages in this digital era, but replacing old financial institutions is not enough to only have high value.Do you think there's a way for bitcoin to compete with some bank services? I use a credit card but I know the only reason the bank has anything to "lend" me was because someone stored his/her money for safe-keeping for close to no interest.
We are still moving millions of dollars and even a few dollars at a fraction of a cent, to anyone in the world. 
