And one can still do the same today, without an "official" gold standard. Anybody can keep their assets / "money" in gold (coins or buliions or ETFs), silver, oil, stocks, bonds, foreign currencies or under the mattress...
Borders were open and money was footloose.
Whoopee! How's that so different from today?
It went where it was treated well.
As Walter Wriston has said, Money goes where it's welcome, and stays where it's well treated. That's a truism that stood for centuries and has nothing to do with "gold standard" but rather with the governments' fiscal, tax and regulatory policies. Right now "money" (USD$ and Euros) and especially "hot money" is flowing out of the U.S. and much of "peripheral Europe" and into Asia, because it's welcome in emerging economies and is not well treated in developed economies. Except when panic hits in other places on Earth and than "money" flows back into USD$ and the U.S. T-bonds.
The classical gold standard, the one that was in place from 1880 to 1914, is what the world needs now. In its utility, economy and elegance, there has never been a monetary system like it.
Yet during that "elegant" gold standard period there have been at least one severe recession, period of deflation, and at least one case of severe financial panic of 1907 which required strong and immediate action and showed the power of one man (Jonathan Pierport Morgan) taking charge of the group of top bankers to save the U.S. banking system from the brink of collapse. That event, and that power, has so shaken and spooked the U.S. government that it directly led to the establishment in 1913 of the U.S. central bank known as the Federal Reserve System, formed and based in part on the model of central bank of England known as Bank of England (aka The Old Lady of Threadneedle Street) which was founded in 1694. Other countries' central banks, e.g., Deutsche Bundesbank, Bank of Canada, Reserve Bank of Australia, all perform basically similar functions.
I generally like James Grant's broad knowledge of financial history, but he is distorting history here to try and "prove" his "gold bug" point and does what's known as "talking his book". There were problems with financial systems and the government deficits, debt and periods of inflation and deflation before and after the "gold standard," before and after the "fiat money" and before and after the formation of the U.S. central bank (the Fed).
If you're going to base money on anything in this day and age it has to be a typical basket of the goods and services a country actually produces.
The Fed was created to save the banks from themselves. The panics you speak of were created (as they always have been) by banks lending out more money than the gold they held in reserve. They failed as they should have.
The New York bankers, though, convinced Congress that the legal ability to create more currency would benefit the country. And, of course, along with that came the power to bail out the banks when they over-extended themselves.
Too important to fail, you know.