Several FinTech startups are trying to fill this gap, connecting the banking system and blockchain technology (and using BTC itself), acting as a payment method. I don't believe that the banking system will take a step to get closer to provide itself this payment technology. I saw some banks starting to develop things using blockchain, but BTC, noting yet.
Banks are ready to accept the blockchain system, but they do not want to take bitcoins. This is not very fair. After all, if banks start taking bitcoin, then it will become much more convenient to use.