I do not think bitcoin can destroy the banks. People do not change their habits easily. They also trust the bank too much. If the bitcoin starts to be used by a few billion people around the world, the banking system could end up.
But the states will not allow it. States always support systems they can control.
in fact it is not possible in present time. because almost all the people of the world are using fiat and the user of bitcoin are still very low. i think in future when the users of bitcoin will increase then it may become possible that the use of banks will decrease.