Let's take it a little further than that.
I can see a hard gold standard working. What I can't see is how we would transition towards it - especially if we don't have the gold.
Higher gold prices. Gold is scarce, yes, but there is plenty of it to facilitate transactions, otherwise history wouldn't have selected it as money, up until recently.
You have argued that people should be free to use any currency they choose. Again I don't see that helping the cause of a hard gold standard. Historically, it seems, fiat currencies tend to displace commodity-based currencies. (The more usual way this "law" is expressed is, "whenever 'bad' money is introduced into a society, 'good' money gets withdrawn").
This is nonsensical, because the consequences of Gresham's law that you're describing are the direct antithesis of freedom in currency - fiat money. Fiat means "by decree". Decrees are meaningless unless backed by violence or the threat of violence, so the very existence of fiat money precludes freedom of currency. I would add that this leaves unresolved what exactly the state would officially accept for the payment of taxes. The coercive aspect of taxation as it relates to what is acceptible for payment is the "teeth" in the decree. It follows that whatever the state demands for the payment of taxes is a "fiat" currency. If the state demands that we first accept paper so that we may satisfy its demand for that paper later on in the remittance of taxes, our freedom to use whatever currencies we choose are impeded in proportion with the size of the state.
This is the dilemma of having freedom of choice in currency.
At least a full reserve fiat only system seems implementable. Ideally, a central agency would figure out how much money needs to be created each year to keep the economy functioning at optimum levels. In practice, politicians would never cede the power of the money press to an autonomous agency. The chancellor would probably want that power for himself.
Once again I vehemently disagree that its ideal for some central authority, be it a presumably accountable politician, or private central banker to issue monetary edicts from his ivory tower. The best monetary policy is no policy, it is using a form of money for which the supply cannot be manipulated.
We've seen politicians cede vast amounts of public power to unaccountable private entities in the past, just witness the modern central bank. The only thing the politician asks in return is the promise to monetize their endless budget deficits, something which central bankers do gladly in exchange for the institutional right to counterfeit money.
Politicians in charge of the money supply? Most people would shout "Noooooooooooo!!!" However, money needs to be created to keep debt levels down to a reasonable level (compared to GDP for example). The natural avarice shown by politicians would actually work in our favour. Ultimately it would be up to the voters to decide how much of their taxes they want to pay directly and how much through inflation.
Strictly as a lesser of evils, I would rather have the money supply managed by a politician than an unaccountable central banker, but this is far from ideal. With regard to limiting debt, I would prefer to have it done by statute, and set the limit at zero.

