In fact, it did so well for so long compared to previous methods, that the Great Moderation is a term in economics for the stability it gave.
Instead of snarkily listing places you think it failed, compare that to pre-Fed failures, and you'll see that the Fed is a lot better than other solutions.
And there's ample economic evidence central banking is much better than anything before it, which is why every single country in the world has adopted it.
https://en.wikipedia.org/wiki/List_of_recessions_in_the_Unit...
So why pick a single event, ignore 50 others, ignore the trends shown in US (and 100's of other country) datasets, covering hundreds of years?
I just posted a decent intro to the evidence. Please read it. The economic evidence for the benefits of central banking versus not having a central bank are so thoroughly answered in economic literature that not a single country is stupid enough to go without one, despite those 100s of countries having a lot of other variety.