This doesn’t make sense in any money system. For commodity money, the supply is set by mining. For fiat, by a Treasury.
How does it not make sense?
In the era of free banking in the US, banks issued their own currency.
I mean exactly that. They issued banknotes (that's why paper money is sometimes called banknotes). The banknotes were denoted in dollars, like bank checks today.
Here's an article with some pictures:
https://thismatter.com/money/banking/history/free-banking-na...
As I recall, they issued the paper version of stablecoins: they were denominated in units of US dollars, but they weren’t government money, and they traded at floating values, typically (aside from many other factors influencing value) declining in value with distance from the issuing bank.
When the Fed lost all credibility with exchanging their banknotes for gold, we had the Great Depression. FDR then defaulted on the gold bonds, basically stealing from the good citizens who had trusted the government.
This was not a cause of the Great Depression. (You are correct on the default, however.)
The free banking era illustrates the problem. Rates are endogenous to the money supply. That circularity promotes a hyper-volatile credit cycle. There is no natural counter-balance we’ve discovered to that tendency. (Apart from ruinous boom-and-bust cycles.)
So there is no market for the interest rate of money that can be created.
If you have a fixed money supply then the interest rate isn't set by supply and demand of funds either but by liquidity preference. As the interest rate falls below liquidity preference people will simply hold cash or keep their money in checking accounts. The interest available for borrowing does not fall all the way to zero. It gets stuck at some positive value. This money is "saved" in the sense of deferred spending but it is not "saved" in the sense that it is not lent out and only available in the future once the loan is repaid, no, it is available today to spend.
The difference between classical and Keynesian economics is effectively that in the former you only have saving and consumption but in Keynesian economics you also have a third state "cash" (including bank account deposits) that is a hybrid of the two. It is neither consumption nor classical saving and this is what's the setting of the interest rate in the open market.
Dieter Suhr effectively argues that this liquidity premium is the effect of money being a social network. Just like Facebook extracting profits from your data, people with cash/deposits benefit from the network effects of money and can sell these network effects for money keeping the interest rate high and if they can't sell them they will try to benefit from them directly (e.g. speculation) as that is more profitable than lending money. Businesses and consumers are the ones creating the network effect so they should be compensated and not the idle who do nothing with their money.
The supply of gold varied, by quite a bit. See the various gold rushes and the resulting inflation/deflation.
I am quite certain they have an accurate high level understanding of the relationship between their supply, interest rates and inflation.
I would also like to point out that there are different types of interest rates. I am not sure what rates you suggest would be set by S&D.
Free market banking is banking in which any bank can issue money. The "supply" they were referring to is supply in the economic sense of supply and demand, i.e. the equilibrium market price of money/debt that would arise from the supply and demand of market participants.
If one farm had a legal monopoly on selling apples, them yes technically they are "supplying" them, but the price is not what the natural price of apples would be in a competitive market absent any legislatively granted monopolies.
This should help as an introduction:
https://thismatter.com/money/banking/history/free-banking-na...
Any bank could go rogue and lend money below central bank/base rate, but because all other banks can "earn" free money at the central bank at base rate this opportunity would instantly be arbitraged away.
Likewise market forces for borrowing are determined by the risk premium on top of base rate, with competition for borrowers arbitraging away opportunities for risk takers (lenders).
No. In Friedman's "Monetary History of the United States" he shows how the Fed setting interest rates was rather erratic and much more unstable than the earlier free market mechanism. The Fed would guess at what the S+D point was, since the Fed was not subject to market forces. This meant they were always late and always wrong.