That is not how "backed by" works. The federal reserve does not need more gold to create more dollars. To define it your way the dollar is backed by cow turds too.
Discussion
Backing means the issuer redeems the currency for the backing asset
The issuer here is nominally the Federal Reserve but in practice the US Federal government
So the Federal Government offering a real asset for dollars is a form of backing (with the caveats that gold redemption is not at a fixed rate & it's a different agency)
I'm not aware of a USFG plan to offer cow turds for dollars
Where should I as a private citizen go to swap cash for a few gold pamps directly from the federal government?
https://catalog.usmint.gov/coins/coin-programs/american-eagle-coins/#oos=true
But you're better off going through one of their 7 or so officially approved bullion dealers, since the Mint individual sales are higher premium & focused on proofs & modern "numismatic" coins as opposed to bullion simple
Eg APMEX, Miles Franklin
140% of spot at US Mint is clearly over priced even for numismatic value.
Apmex and so on are private businesses exchanging goods, not the government.
I agree. But, you *can* turn dollars into specie directly at the Mint, which is (with the caveats I mentioned) redemption.
If Federal Reserve Notes are theoretically worth 42.5 $/tz, then gold at 2000 $/tz is dramatically overpriced. 2700 $/tz is even more so, but obviously by lesser proportion.
The official brokers are private, but they get the current coins directly from the mint - you can order mint-sealed tubes of current-year coins. Does the fact that dealers act as a middle-man actually matter economically?
https://www.apmex.com/product/258634/2023-american-silver-eagles-20-coin-mintdirect-tube
If you refuse to see the difference between allowing a market to exist and a guarantee that a bill can and will be exchanged for a fixed amount that does not change during its lifetime, I cannot help you.
There's a difference, as I have twice acknowledged.
But US mint buying back "dollars" is not merely "allowing a market to exist".
The fact that someone somewhere wants to give up gold for "dollars" is not backing or relevant. The fact that the issuing government of those "dollars" will make that trade is relevant.
Everyone, except the people who stand to profit from printing USD and you apparently, agrees that to be backed means a fixed exchange rate and that every dollar could be exchanged without running out of gold or changing the exchange rate. That is not the current state.