Up until the beginning of the year 2018 when the Korean government was threatening tighter regulations on cryptocurrency, banks had been some of the biggest investors in crypto. Most banks, like other institutions, are tapping into the potential that the blockchain technology has to aid them in servicing their customers.
Banking, as with other services or products is 'adapt or die'. Remember Kodak and all the dinosaurs that refused to change with times. Only banks that refuse to adapt can become obsolete. That said, while we embrace blockchain and crypto, it is worth noting that there are people who will NEVER be part of the crypto world, because they won't/or can't. For them, the banks will continue to exist.
I agree with this if some banks are so dumb to think that people are not going to change and adopt this new technology then they are going to disappear, it is the same that happened to the US automotive industry they thought their American clients will always buy American products just because, and that lack of vision is why most of them are close to bankruptcy.