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And how exactly did that work in Rome, pre-revolutionary France, Weimar Germany and so on?

Surely, you can provide examples of fractional reserve/fiat money systems leading to stability over the long run, without cracking up in ruin and revolution?

And how exactly did that work in Rome, pre-revolutionary France, Weimar Germany and so on?

It didn't; those nations and times had very different systems. Their money supply was directly controlled by the government, and was increased to pay off debt, rather than controlled to moderate inflation. Rome and 18th-century France existed before any sort of modern understanding of economics or inflationary processes, and Weimar Germany was saddled with enormous debt loads they had no idea how to pay. Since then, Milton Friedman has come along and taught us that inflation is a monetary phenomenon, and our government cannot directly control the money supply to pay off debt; the Federal Reserve controls the money supply, and as they have no interest in debt repayment they are free to target inflation, which they have done successfully for the past 20 years. Also, it should be noted that of your examples, at least Rome was on a gold/silver standard; the emperors just devalued the precious metals as easily as Weimar devalued paper money.

Surely, you can provide examples of fractional reserve/fiat money systems leading to stability over the long run, without cracking up in ruin and revolution?

The United States, 1973-present and continuing. Also all other modern first-world economies. Now, perhaps you can provide examples of nations that sustain modern, growing economies without a banking system or a means to grow faster than the increase in the government's gold supply?

Great Britain has not had a revolution since 1688 four years before the founding of the Bank of England. France's revolution was not caused by fiat money it was introduced during the revolution and theoretically based upon the lands confiscated from the Church.