Banks are going to stay but will eventually change significantly, guess to a somewhat extreme extent, totally unpredictable for now.
Once people start putting more power in crypto (i.e. laws of math) & each others and less in traditional mechanisms of trust between financial counterparties, a paradigm shift in society's mind would become inevitable.
In my opinion banks will have to accept cryptocurrency for their survival. If they do not use crypto in the future, they will disappear from the markets, because people are withdrawing their money from their bank accounts and putting in banks because banks use peoples money for themselves and give nothing or very small profit to customers.
Nothing happens to the banks anyway. They were, are and will be as long as the state will exist. Even if the banks did not work with cryptocurrency, they would still feel great. Cryptocurrency will not have such a serious impact on the financial activities of mankind, as many imagine it. Cryptocurrency will always have a secondary role compared to the usual currency and will never replace it. It will be used primarily by citizens, and not by states and their bodies. Even business structures are unlikely to massively use cryptocurrency due to its high volatility and poor documentary evidence of ongoing transactions before tax services and audits. Still, banks are better suited for business structures.