There’s nothing special about banks, or the banking system, that suggests it should not be nationalized.
The money system is a national function already. Congress “coins money, and regulates the value thereof” and “issues bills of credit on the united States”, and no State may “make anything but gold and silver coin legal tender in payment of debts”.
Banks and bankers are supposed to be servants of the above, not masters.
Because the central government consists of servants and not masters?