I think banks are controlled by Goverments, and Blockchain won't. If Goverments issued own cryptocurrency based on Blockchain, it would replace some bank functions but not all of them.
It is the opposite actually, Banks control the government. This differs in every country but mostly, it is the scenario. Some banks are semi independent but government wants to control it too. If they issued their own crypto currency, it will never replace any bank functions since the approval of it will also roll through the banks like what happened in India in the past about banning crypto currency. Blockchain will be centralized, public records can be available online which governments can review and assess and they can create laws, new rate of taxes and I can see some security flaws so this will never happen for now, that's for sure.