The currency issued by a country is a lot like the shares issued by a company, in that both are arbitrarily issued and the supply can retracted or expanded by them at any time
The main difference is that shares pay a dividend whereas currency does not. Though if you consider the banks to be part of the government1 then currency does pay a dividend in the form of interest.
Another difference is that shares often come with voting rights while currency doesn't directly come with voting power. It can of cause be exchanged for votes by a variety of means but that isn't the same since it involves selling the currency. With shares you get to vote and keep the shares.
Banks are so tightly regulated that they effectively have no real control over anything that they do. And if any bank did do something unusual they would probably get a slap on the wrist very quickly. Whenever, I go to the bank to get cash out they treat the cash like it's an assault rifle that I have no business possessing. This behaviour is clearly at the behest of the government who would prefer cash didn't exist. Banks should like dealing with cash since it gives them an opportunity to charge fees for a service.