I'll replace your question and I guess its better if you'll ask this "Will the banks use blockchain technology?"
I doubt it that the banks will be gone in the future though we got crypto, we can fully ignore the banking system and stick to crypto's as no need for an application to open a bank account, no requirements needed and no more waiting days of creating our own bank accounts. Our wallets are already our bank accounts.
There's also a tendency that the bank will join this crypto revolution as they have no choice to compete against it.
I am thinking the same banks will be there anyway but they can not ignore crypto. Banks are slow, less trustable indeed.(not all of your money is granteed by the banks thats why they are less trustable then your own blockchain wallet).. People needs to feel that their hardly earned money is secure place while they are sleeping. Because of the security issues banks will never replace blockchain but they will use blockchain technology everyday life near future.