Why would the same principle not apply to any situation where a person owns two kinds of money (both fungible, liquid, universally accepted), regardless of exchange rate rules? People will always prefer to hoard ("save") the better of the two and pay ("get rid of") using the worse of the two.

Because in an efficient market, if one of the currencies is preferable that will already be reflected in the price. If, based on public information, you would rather hold currency X than currency Y, then so would your counterparty in the exchange, so the buying power of currency X would rise accordingly.

Gresham's law applies when a legally fixed exchange rate means that the price can't reflect the difference between the two currencies.

I'm not going to get dragged into a discussion on "efficient markets". You win by forfeit.

Efficient markets was just a simplifying assumption to make my point brief, but the second sentence of my explanation does not rely on any more assumptions than Gresham's law does.

In any case, I recommend that chapter of Hayek, it's a quick read and you might find it clarifying.

The difference is that someone is not legally forced to accept the inferior currency. All your attempts to horde the better currency can fail when the person you want to buy from either refuses the inferior currency, or accepts it, but at a price that accounts for the difference in relative value so there is no difference.

Edit, this used to say, but that is wrong: The difference is that the which is best changes over time, so you change which one you are hording based on conditions.

Nice! Argentina had currency controls and this effect happened immediately.

Gresham's law could happen if the governments...banned bitcoin!