Treating dollars as non-fungible because you might be interested in a particular serial number (and there are people who do this) is equivalent to various "colored coins" schemes on the Bitcoin blockchain, where you treat Bitcoin that's passed through certain wallets as being non-fungible with other Bitcoin. I would not call either of these more or less fungible, because the majority of people who use dollars or Bitcoins don't care about the fungibility beyond maybe "is this stolen property".
Also, because inflation is a systemic part of the fiat money design, the fungible coins become less and less significant over time. In 2022 dollars, a quarter was worth $7.48 in 1913. We removed the half penny from circulation when it was worth more than a modern dime.
This also applies to any law that establishes a lower bound on money subject to some kind of surveillance, like the $10,000 reporting requirement on flights. When that law was passed, $10,000 was worth closer to $70,000 today. Because the value in the law was set statically, every year the slow grinding ratchet of monetary inflation includes more and more people and use cases into its jurisdiction, with barely anybody noticing.
Monetary inflation provides a great mechanism to slowly boil the frog.
I see you are repeating something patently wrong and even adding some equally wrong "spice" to it, like that cash notes are non fungible by design, which is somehow "literally an inseparable part of their physical existence". This despite currency (in any form) predating the formalized concept of fungibility.
Money is fungible by every (literal) definition of the word, whether banknotes or coins. Being fungible doesn't refer to the physical aspect of being absolutely identical but to its value. Money exists to be fungible, fungibility is literally one of the big things that make money work. Going even further, money is probably one of the few things equally fungible whether new or used, and sometimes even old/outdated (think retired currency which can be converted to currency in circulation).
Whether coins or banknotes, they are interchangeable from one to another regardless of serial or the year stamped on them. And almost any other two new "identical" products are just as fungible: two loaves of bread, two planks of wood, two pencils, or two cars (not the case for used products). They're all mass produces, quasi-identical units.
And the serial numbers? They're used mainly for uniquely tracing the note and don't affect the fungibility in any way. The proof? Randomly pick a banknote every time you pay for something. If it works every time either you're the luckiest person in the world, or they're completely fungible.
Because money can be readily traded for anything else it is effectively a joker, equivalent to any other card but with the ability to respond to nearly any situation.
This means people value money itself slightly more than the things you can buy with it. Since money doesn't spoil, this tricks our monkey brain into hoarding the stuff, no matter how much we already have, it is a type of "desire" that can never be saturated. This is known as liquidity preference and since money is worth more than the things it can buy, giving up liquidity must be compensated by paying for the loss of liquidity, this means the minimum interest rate gets stuck at a floor.
When you consider that the optimal interest rate is 0% when markets are saturated we are in a pickle.
So instead we decided that loans create new deposits, we no longer have to ask anyone to give us their money, no one has to give up liquidity, hence why interest rates are below liquidity preference.
Of course the problem with that is that as long as yields are optimal and markets are saturated, you are going to need to expand the money supply. This in itself doesn't necessarily lead to inflation but to stave off deflation, central banks decided to target 2% inflation, this lifts the profitability of companies in the real world closer in line with liquidity preference, in other words, we need inflation to neutralise liquidity preference.
Yes now go ahead and introduce negative interest rates on cash so we can stop messing with the unit of account.
By the way, inflation is a systemic part of any permanent money system, not just fiat.
People mine on Blockchains because they think spending electricity is a better way of getting Bitcoin than trading with existing Bitcoin holders.
People mine new gold because they think it is easier than trading with the existing owners of gold.
Even with a perfectly fixed money supply, there will still be inflation and deflation as people spend their savings faster than others want to save or as people save faster than others want to spend. You can't force eliminate inflation by decree you can only eliminate it through cooperation. The constant up and down price swings of Bitcoin are inflation and deflation. Bitcoin doesn't solve the inflation problem.
