On that view there has never been a 2a system. No one would honor a private bank note that was not backed by some asset or government fiat. Such a note would, quite literally, be worth no more than the paper it was printed on.
There's a difference between people freely choosing what assets are acceptable to back a given currency and having many currencies floating in value against each other, or the government deciding what each currency can be backed against and at what value (the National Banks had to accept each other's currency at par value).
Yes, of course. But if you have currencies backed by too many different kinds of assets those currencies aren't money any more, they are tokens in a barter economy.
