You’re right. It would be correct, but for the Fed.
If we ran out of Treasuries (the government paid them all off) the people would be about $15 trillion poorer (I don’t know where we’d get all that money, since the total amount of money in bank deposits is only around ten trillion, but whatever), the Fed could continue to print money by buying private securities. Of course, assuming the Fed were buying at market prices, that would have a net-zero effect on private wealth. There would be more dollars, and fewer - I don’t know - corporate bonds. Or mortgage bonds.
But if the public was trying to net-save (spend less than it makes) taking away private savings vehicles wouldn’t help.
The Fed is also taking away savings vehicles by buying Treasuries, but the difference is the Federal government - if it’s good policy - can always print more Treasuries. It’s not constrained, the way a private business is.
It can also buy back Treasuries (directly or indirectly from the Fed) if it chooses to tax more than it spends. Which makes both the money it spends buying the Treasuries, and the Treasuries themselves, disappear, simultaneously.
Taking away the role of the Fed for a moment (which does make everything more complicated, though not fundamentally different) when the government taxes more than it spends, it takes financial wealth away for the private sector. When it spends more than it taxes, it puts financial wealth (Treasury bonds, for example, or just plain cash, if the central bank is buying the bonds) into the private sector.
You’re right that if your economy has lots of problems - if it’s not running at full capacity because of (for example) corruption; poor or non-existent infrastructure, or an illiterate or otherwise unskilled workforce, just printing money isn’t going to solve those problems.
But there are countries, like the US, where the constraint on the economy is none of those things. Instead, it’s lack of demand. It’s people attempting to save more than their income. In that specifics situation, the solution is to print more money, or more near-money savings vehicles, like Treasury bonds. In the best of all worlds (assuming you have a central bank) you’d do both. You tax less, spend more, print Treasuries, and then the Central bank would buy the Treasuries. (Or at least some of them.)
The end result would be that you would satisfy people’s demand for financial savings, so they would spend more, putting more people to work, which would result in the production of real wealth. (Employed people producing goods and services.)
Banks meet payrolls out of the profits they make selling loans. If banks didn’t spend the profits they get from making loans - by meeting payrolls, or paying shareholders, or building tall buildings or whatever, the economy wouldn’t work. But anyway, banks make meet payroll out of profits, not by creating new money.
I understand that: in macroeconomics savings is the same as investment (in a closed economy, such as the world as a whole.) It is not what ordinary people consider saving: spending less than you make. In fact, in a country without international trade, or one with with a balanced trade (X=M) there is no “saving” in the sense of people having spending less than they make, because by definition everything must be spent to be earned, and therefore all spending must be classified (more or less arbitrarily) as “consumption” (immediate) or investment (something that will last a long time).
Yet we do have a trade deficit, and have had one for a long time. The trade deficit consists of other countries accumulating dollars, while we accumulate stuff from their countries. That means, according to the equation, our savings are negative, have been negative for a long time, and will - presumably - will continue to be negative for some indefinite time in the future.
Now there’s something that bothers me here, and maybe you can explain it. Our negative savings rate is the accumulation of dollars by others countries - which also represents their savings rate. But the accummulation of dollars isn’t savings in macroeconomics, right? Savings = investment, right? And investment isn’t spending less than you make, it’s making things that last a long time. So if, for example, China, or any country, is accumulating dollars for the sake of accumulating dollars, doesn’t that mean they’re not investing?
In other words, if you’re going to define savings as spending money (on things that last a long time), but then define savings as accumulating dollars (not spending them) in another part of the same equation, isn’t that self-inconsistent? What am I missing?
Have to stop for now. Will try to respond more later.