Putting central banks out of business would enormously increase productivity, because fiat currency has encouraged everyone to live fragile lives and discount their future for the present, because the future is always uncertain under a fiat standard!
But, is central bank really going to be blamed for being a store house to fiat? Banks are merely existing because of fiat, no fiat no bank

. Moreover, fiat that is not housed in the banks are not excluded from inflation. You keep your fiat under your roof, it is still going to be inflated.
With the history of fiat, at a time before it, there was trade by barter and other means until modernity gave birth to fiat.
I think the main culprit of fiat is the government, I mean the policies of government that have successfully caused inflation and hyper inflation or maybe it is just the nature of fiat, an inflationary currency. Which means no matter how the government manage it, an addition of printed currency would likely cause a bit of change in economic status quo inflation and causing the standard of living to drop presumably.
Technology and growth have brought decentralised digital currency and also centralised digital currency/cryptocurrency of which the centralised coins still are influenced, disrupted just like fiat. So I don't think bank is the
because fiat currency has encouraged everyone to live fragile lives and discount their future for the present,
reason for this but fiat itself which is inherently inflationary.