That is probably the main reason why I'm so partial to ragged National Bank Notes like the one below.
There was a time that this was true but that was back in the sixties. Now they are only worth face value.
Yes, they are redeemable, but not in exchange for gold or silver. They usually have more value as a collectable note than face value.
The 1923 series were called horseblankets because of their large size As far as small sizes, the US issued fractional notes that were pretty small, the only one I have is this: