Uh, no it wasn't. From the very first search result I got on Google, a rough CPI measure of inflation would indicate that the US dollar was worth twice as much in 1900 as at 1800, a total inflation of -50% [1].
Now, that's not the most accurate assessment of inflation because the very concept of a single number for "inflation" doesn't work out well when you start trying to compare monetary amounts across decades, and it especially breaks down when you're bracketing the Industrial Revolution. But the broader point here is that the US dollar wasn't some mythically stable thing during the 19th century that somehow galloped out of control in the 20th century.
> and there weren't any financial collapses in the 1800s comparable in magnitude to the Great Depression or Global Financial Crisis.
This is "never-cracked-a-history-book" levels of incorrect. Severe depressions recurred about every other decade, and practically every decade had some sort of Global Financial Crisis-esque financial meltdown. Back then, most of these were called "Panic of <year>" instead of "depression" or "recession", until you got to the Long Depression, which was called the Great Depression before the Great Depression itself actually existed.
If you're familiar with US economic history, far from being a century of economic stability, 19th century American history was an economic roller coaster of soaring heights and terrifying crashes and the transitions between them being sharp, sudden, jarring, and without warning; by those standards, 20th and 21st American economic history is tame. (Indeed, commodity money is one of the causes of the rollercoaster nature of the economy, far from being a moderating force.)
[1] Yes, the sign is right. Because, again, bracketing the Industrial Revolution.