You're forgetting something rather big: I can buy gold right now because of legal tender laws.
*Edit*
And I still gather that Gresham's Law would provide a smooth transition between the two currencies? I don't care to figure out what variables to use, but over time this would mean a general curve if modeled correctly.
If the value of the USD dropped to zero overnight, you might have a point. The removal of legal tender laws isn't going to make that happen. Basically, we need to allow what's known as Gold Contracts, which legal tender laws make impossible. You do something for me, and at some future time I must pay you X amount of gold, or sheep, or whatever. What a legal tender law says that all things have a dollar value, and if a party can't settle a debt make in XYZ, he can give the equivalent dollar amount.
The dollar has value, as does every fiat currency, because people know others will take it. You'd surely be able to buy gold with it. Also, what are all these gold holders going to do with it all? Sit on it? They need to eat too. Gold holders would spend it, putting it into circulation. Even if they're making more gold, there's still exchange going on.
Maybe the fed could actively destroy the monetary base of dollars to maintain their value during the transition. Either way, it's not an argument against allowing people to use other things for money.
Did you know there are several alternative currencies in America now? Interestedly enough, several are labor-theory-of-value marxist based ones, like Ithaca Hours.
https://www.ithacahours.com/intro.htmlThe problem is Gresham's Law prevents their widespread adoption.