Banks & governments are going to have to start being bitcoin friendly in the next 10 years or they can just sign their own death cert right now. Bitcoin is the present & definitely the future, adapt or get left behind.
It's not obligatory. The banking system is fully under the protection of each state and, in fact, is part of the state system of power. Therefore, as long as the states exist, nothing threatens the banking system. States have sufficient mechanisms to eliminate any difficulties in the way of their banks.
At the same time, banks have long appreciated the benefits of digital money based on blockchain technology. They will definitely implement it and are partly already on the way to this, however, the financial system does not like haste, it transforms very slowly. Of course, this will be a completely centralized and controlled by banks currency.
Even without addition of bitcoin into the service list banking services is taking place in a much effective manner. Banking services are limited, because beyond certain volume of transaction it requires lot of process. When it comes to cryptocurrency, it is possible to transact any volume of fund with ease. As most users mentioned, it can get added as a store of value which helps the banking process more ease.
In my country three banking transaction upto $750 is free of charge per month. Beyond that for every transaction it cost a minimum of $1 and tax on the transaction cost. When it is compared to bitcoin, right now bitcoin transaction costs big.
On considering different facts it is true that banks will adopt the technology and add bitcoin related services. Even without bitcoin adoption banks will survive and facing death won't happen as easy, because state have control over the banks.