The banks are conservative and would really find a way to hedge against inflation. They'll surely diversify their depositors money but only to those investments that they have an assurance.
For some people might say something like that will happen, but maybe there will be a way to deal with inflation without having to run to bitcoin, inflation has always existed even before bitcoin, and that problem can also be solved. we just don't know for sure how it happened. CMIIW
There is but it would be a lot of methods that they have to add at the same time. But bitcoin as their choice, some of them really are having interest on it but we can't be sure if many of them will.