
The Mystery of Banking is a great expert analysis of the modern fractional-reserve banking system and its origins-how it is unstable, how it exacerbates business cycles, and how it causes inflation. This book lays out the devastating effects of this most common form of banking on the lives of every man, woman, and child.
To your point, however, the US has had prosperous period of its history with free (I.e. no central/federal control) banking. See Rothbard's "The Mystery of Banking."
* "End the Fed" by Ron Paul
* "Economics in One Lesson" by Henry Hazlitt
* "The Mystery of Banking" by Murray Rothbard
* "What has government done with our money?" by Murray Rothbard
* "Debt: The First 5000 Years" by David Graeber
If you would like to read a thorough argument about how fractional reserve banks and the Federal Reserve are scams, read "The Mystery of Banking" by Murray Rothbard. Google it and you will see it is available for free at mises.org.
For some reason this subject is very polarized and I get downvoted whenever I explain this. Don't downvote me just because you are uncomfortable with what I'm saying. Note that I am not ignorant. I have learned about economics. It just so happens that when trying to understand the issues myself, I have arrived conclusions that are not mainstream. But they are the correct conclusions in so far as I presently understand.
Too dense for me, reading pace was too slow. It's good, but reading it is hard work. I'd recommend "Mystery of Banking" first, which is smaller in scope, easy to read, very informative.
Free here: