Like governments, there are many scenarios as to how banks will respond. They are already experimenting with adopting blockchain technology. But, in practice, banks will soon lose their monopoly on issuing expensive money. Many of them will be very upset and will do everything in their power to maintain that privilege. But more and more leaders inside the banks themselves understand the deep systemic problems built into debt issuance of money, and are looking for ways out. The original purpose of banking (as a profession), is that it is to help people wisely manage and invest with their savings. It is a relatively recent historical addition that banking has become a for-profit business which makes money by issuing money.
Some banks will hopefully be more clever and visionary than others. They will see a wonderful opportunity to create new, useful services in the open currency world. They will return to their original mission statement and become trustworthy again.