The fault in your thinking is that commerce can’t multiply money. Money created by banks, the only authorized licensee to create dollars, cannot retire the debt that it was created from. This is because banks don’t create permanent dollars, but instead “credit accounts” for qualified borrowers. The Federal Reserve loans them dollars to make inter-bank transfers possible, but those are “liabilities” to the banks, not assets.
The banks will use a portion of the borrower’s “real dollar” payments to pay down the Fed liability so that the principle is always balanced, keeping any interest and fees as profit. As the last payment is made all accounts except the bank’s bottom line will equal zero, so no actual “money” is created by the bank or Fed to represent the activity the loan generated.
The counterbalancing assets are the loan contracts the borrowers sign, which makes it all balance out. Everyone’s liabilities are someone else’s asset in the banking world. Only the monopoly issuer of the currency can produce the high power money needed to store value from commerce or be net saved. For the US that issuer is Congress, and it must deficit spend to do so, or any gains of the private sector are consumed by taxation and nothing is left to store value or retire private bank debt. A balanced budget for the government also means the theft of all resources the government “purchases” from the private sector.
But then, allowing the government to provision itself without a revenue stream is the primary purpose of public money, just as the purpose of taxation is to create demand for the money government can produce at will, not to “fund” anything. Taxation also destroys money when it comes full circle back to the Treasury. This is as easy as creating a “debt” entry in Treasury’s balance sheet for every dollar created by Congress in the private sector. When the dollars received from taxation get together with that debt entry they balance to zero and “cannot” be revenue for anyone.
This offers effective inflation control by drawing down the money supply as well, which would be negated by actually “using” the proceeds to spend. Spending by the federal government creates money and taxation destroys money, making it all much neater than the way almost everyone thinks it works. Creating the “illusion” of the people paying for their government with their taxes works very well to prevent them from demanding the luxuries enjoyed by the owner class/capitalists and divides them between makers and takers. In reality, it is the spending of the federal government that “funds” taxes (and borrowing). One cannot collect or borrow what doesn’t yet exist.
Your point of a separation existing between “real” value, which is the goods and services produced to garner money, and the money itself is valid. My point is that the “people” do control the money supply, even if they don’t think they do. That control is called democracy, which is why the elite and their lapdog politicians work so hard to keep the illusion intact with distractions about the deficit and debt, both of which are simple accounting entities. The money is a no-cost commodity we can never run out of, and we can afford anything that is available for sale priced in dollars. Any misery in this system is entirely a political decision, not economics.
