Soon, and I am looking forward in that possibility. Banking, for me, needs blockchain technology for a better transaction security and records. Banks just need to accept the fact that blockchain is an emerging technology and they need it the more than anything else.
Whoever understands this fact and start implementing better technology into the system they will survive in this competitive world otherwise they may end up like a Kodak company. Now, these banks may be at the top but if they don't follow new technology then no one can help them in the future. We will see more and more companies start using this blockchain technology soon for better services.