I believe this is profoundly incorrect, though it is commonly believed to be true. To understand why it is incorrect one only has to consider that nowadays all money is "printed", and how much money would be available to carry on commerce in the private sector without any government spending at all.
The other parts of your post are interesting to me but for now, since I'm somewhat time constrained, I'll choose to reply to just this.
As you started out with the US as an example, I disagree that nowadays all money is printed. The US had money historically without the need for government debt, exemplified by President Andrew Jackson who paid off the federal debt entirely.
The US dollar was defined as a weight of silver (371.25 troy grains) with the Coinage Act of 1792. At the same time, Congress established a gold weight for the dollar and set the ratio to 15:1. In 1849, the ratio of silver to gold was changed to 16:1. Both metals were legal tender. The system existed until 1913 and money at the time wasn't printed. Whatever money stock existed at the time still is part of today's US dollar supply.
Spending is not taxation because no taxation is needed for government spending.
We're using different definitions here. The government taking resources from the private sector is called taxation by me. It could also be called levies, fines, tariffs, or theft.
Government spending puts money into the economy. The Government requires no taxation at all to create new money and spend it into the economy. In fact, it does this every time it deficit spends.
I love how Keynesians can make it sound as if this were a good thing. Any time the government deficit spends with the Fed's help (i.e. not borrowing from let's say private citizens) it destroys the value of money. Any time printed money is spent by the government, it exerts an inflationary force on prices, without fail. This doesn't necessarily mean that prices rise, it could also prevent a price decrease that otherwise would have happened thanks to economic progress.
In any case and by doing so, the government deprives the private sector of resources and redistributes them. It's taking stuff from the people and likely squandering it, not adding anything. Only in meaningless nominal terms is "money added", in real terms purchasing power is destroyed and resources are redistributed and likely misallocated.