A free market in money is my vote as well. If you see that your government is inflating its money supply and as a consequence, you purchase gold, you’re trying to protect your purchasing power. However, later on you want to spend your “gold” so you convert it back to your government’s fiat money. Let’s say that you bought 1000 fiat monetary units of gold and were able to sell the gold for 1250 fiat monetary units. In many, if not all, countries you will be taxed on that extra 250 units. This puts gold and any other form of non-government-approved money at a significant disadvantage. A free market in money would repeal capital gains taxes on gold, silver, etc., and allow parties to individual economic transactions to use whatever form of money they like.
Repealing legal tender laws and capital gains taxes wouldn’t necessarily eliminate fiat money around the world. If you are exporting products to Japan and they refuse to pay in anything but fiat yen while you prefer gold, then you make arrangements to have the yen converted into gold. If you are importing products from Japan and need to pay them in fiat yen, you are free to exchange the necessary amount of gold into fiat yen in order to conduct the transaction.
As far as taxes are concerned, if your government wants you to pay in fiat pesos, fiat dollars, fiat yen, or fiat whatever, you simply convert your gold or otter skins, or whatever you value as money into whatever fiat paper your government requires.
The government doesn’t have to back its money by gold or even change its unit of money. SImply by repealing legal tender laws and the capital gains tax, people would naturally prefer to save their money in the most stable monetary medium possible rather than fiat money which can be devalued or even defaulted upon.
As anyone who has one or more gold or silver coins in their possession probably knows, precious metal as money ‘feels’ more valuable - you think a little harder about parting with gold or silver valued at X fiat monetary units than you do when parting with the X fiat monetary units themselves.