Earlier quoted context omitted.
My understanding of economic history, including the 1870s (but many other busts, too), is quite different. Can you cite a source? I happen to be reading "A History of The World Economy", by James Foreman-Pack. It contradicts you at every turn (Chapter 6 esp) and notes there was a time when the U.S. was the odd man out, lacking a national bank and suffered more severe downturns than other nations, amongst other things…
"And the Reserve System, established in response to monetary instability, had the power to exercise deliberate control over the stock of money and so could take advantage of this possibility to promote monetary stability. That conjecture is not in accord with what actually happened. As is clear to the naked eye in Chart 1, the stock of money shows larger fluctuations after 1914 than before 1914 and this is true even…
No period (before 1914) is given by Friedman. This matters because, as my source is careful to say, a remarkably rigid system of international currency exchange rates had been formed before the WWI. This wasn't an accomplishment of the U.S., nor was it entirely safe, wise, or productive.
Of course, rather by definition, if multiple currencies are all convertible to gold (as they were pre-1914) they rise and fall in exact sync with each other with every whim of the gold market, every gold discovery, etc - until one falls off the cliff and has to renounce conversion - but that hardly means no whiplash!! In fact it means countries are less insulated from each other's economic troubles, more of a monoculture than a robust ecosystem - and, as stated, every country's economy is whipped about by anything that changes how easy it is to get gold out of the ground or increases or decreases consumption of it, including fashion and improvements in dental technology. Also, even the severest depression won't be reflected in the exchange rates. And it was those downturns, that were the topic.
Stable exchange rates have a trade-off; and they certainly don't prove economic stability or the absence of downturns at all. It's more like watching a team of acrobatic aircraft: they all maintain their wingtip distance strictly, and that's fine: but if one plane goes into the ground, they all do. Being in close formation isn't a proof you're not headed for a mountain or the ground; because it's not the kind of stability that has anything to do with that most important risk. Ditto rigid exchange rates.
What changed in 1914 was war. There was no intellectual decision that gold convertibility was unfashionable - war breeds inflation, necessity made conversion a hindrance to the war efforts. That international confusion (and therefore the resultant fluctuations in currency exchange rates worldwide) wasn't created by the American decision to have a central bank, for goodness sake. If anything the arrow of causation went the other way.
If Milton finds it hard to believe that the war-to-end-all-wars might have caused a wee bit of currency turbulence, so it had to be the U.S. finally creating a Federal Banking Institution that did that all over the world, he's rather isolated in that position. But of course, he's slyly leaving that leap into the abyss for the reader to make.