The US deposit insurance via FDIC was created close to the start of the Great Depression and did _not_ prevent the rest of it.

For something that did stabilize economies, see eg the Canadian free banking experience in the 19th century (https://www.alt-m.org/2015/08/08/thats-right-famously-sound-...), or the Scottish or Australian free banking eras.

What made the depression Great were eg FDR's high wage policies, and the American Feds tight money.