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Anyone care to make a case for it?

Why would any country want to abandon control of its currency valuation?

A national government can decide to revalue or devalue its currency in order to stimulate or throttle back its economy. It's one of the levers a central issuing bank can employ, along with interest base rate and the amount of money in circulation.

If the central issuing bank promised to exchange any of its issued money for a fixed quantity of gold, whenever a holder of the currency presented banknotes for exchange, they'd lose that lever. If the market sometime decided that the bank was incapable of fulfilling its promise then a run on the bank could destroy its gold reserves and leave the bank and the currency valueless. What country would be so reckless? What would they gain from making the promise in the first place?

Doing a quick calculation on wikipedia data, the U.S. has less than 500 billion dollars in gold reserves.

Meanwhile, the stock market for example is valued at -- what -- trillions of dollars? (It's backed by the companies, technologies, etc represented).

So if we move to a gold standard, I presume someone will need to get a shovel to match the value of the market to as many shovels full of gold? Otherwise, what are these market dollars tied to? Any dollar (additional value) created by market would need to be backed by the metal in the same quantity of value before such a transaction could occur. Otherwise we have a contraction in the money supply.

Of course one could take the 500 Billion in gold and arbitrarily say it's now worth trillions of dollars to fill the gap. Though this is no less of a fiat money system than just printing money in the first place. And after that decree, the monetary supply is locked into being match dollar for dollar with the mining the metal.

If the currency is tied to anything, I'd think something like "1 penny == 1 calorie" might make more sense. A calorie has use as both food and machine energy.

That would cast a favorable light on obesity too, fat would be worth gold (or gold would be worth fat as it were).

Ah, I hadn't considered that. I suppose the other side too, is they may then start taxing a person more depending on BMI.