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.