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why would it be better to allow a government to do it?

Well until the Federal Reserve the government printed the currency and did not pay interest on it. I would, of course, prefer to have no government money and I hope we see that one day soon.

At one time, not too long before the federal reserve, banks printed their own currency. That MIGHT be why there were called bank notes. What they were in reality were the monetary equivalent of ware house receipts. The banks had your money...you presented them with a bank note, they gave you the equivalent in gold or silver.