First, I am not sure whether you are perhaps confusing the US with the US government? The current account balance is not the same thing as the budget balance. There have been very few times in history when the US government has run a surplus, so you may be confused about that.
In fact, the better private industry is doing, the lower the deficit should be. That's because more money is being made, and more taxes are collected.
That's true, but the causality only runs in one direction. People seem to believe that if the US government attempts to cut its deficit now, that private industry will be doing better as a result. That notion is ridiculous. The causality works only in the other direction.
The difference between the past and present is that now the deficit is larger than it has ever been in U.S. history, by a very wide margin.
So you get big numbers. Big deal. Big numbers alone do not inherently indicate a problem.
It does make sense to investigate them. However, if there is a problem, then the big numbers themselves are very unlikely to be the root cause. If you stop at the high budget deficit and say "we need to reduce that number, no matter what", you are very likely to make a mistake because your analysis of the situation is incomplete. And no, hand-waving and pointing at incompetent politicians is not a complete analysis of the situation.
There are assets that equal liabilities, such as bonds or accounts receivable. But as a class, assets do not equal liabilities. If I own a factory worth $50 million, then I have equity worth $50 million. Nobody owes me $50 million for my factory.
This is why I used the adjective "monetary" in monetary assets.
IF a government needed to provide monetary assets such as quantitative easing, there is absolutely no requirement to run a deficit to do so.
You are confusing purely monetary operations with fiscal operations. Quantitative easing is purely an asset swap, it does not change the net asset position of the private sector. The only way for the government to provide an increase in net assets to the private sector is by spending more than it taxes. That's a simple mathematical fact from accounting.
Keep in mind that most countries can't run deficits in perpetuity. If a country like Brazil had a deficit the size of the U.S. they would go bankrupt.
A monetarily sovereign government cannot go bankrupt even when it runs a sustained deficit. It may cause inflation, and it may cause the country to run excessive net imports, which would cause their currency will drop relative to other currencies. But that's not bankruptcy.
Japan (which you mentioned later) is actually a good example of all this. Their government debt is beyond 200% of GDP, without any signs of financial trouble even at the distant horizon. The exchange rate of the Yen does not drop. The reason for this is simple: despite the persistent government deficits, Japan is not a net importing country.
In general, I have the impression that your thinking is a bit muddled. For example, you write: The U.S. government, and only the U.S. government can freely print its own money to pay its debts. ... But eventually debts have to be paid.
Yes. By printing money. The US government always "pays its debts" by "printing money". In fact, both US treasuries and US dollar bills are just different types of debts of the government. They differ in maturity and coupon. So the US government "pays its debt" by exchanging one type of debt against another type of debt. Big deal.
If you really thought things through, you would realize that the solvency of the government is not the issue. If there is an issue, then it lies in the potential of inflation that is caused by the accumulation of large amounts of assets in the private sector. If there are large amounts of non-moving financial assets, then there is the potential of a (non-sustained) burst of inflation if/when those assets suddenly start moving simultaneously.
But that is not a function of the size of government debt - it's a function of the size of those assets. If you are truly worried about this issue, then the correct reaction would be to look for ways to eliminate those assets, and cutting government budget spending certainly isn't going to help there. You'd have to tax those assets away, or preempt the inflation by creating inflation yourself, for example using additional government spending that ends up in the pockets of people that do not have large accumulation of assets.
You can also just do nothing. Inflation by a sudden movement of existing private sector assets is a very rare event (think end of the Second World War), and in any case, it is a one-off event. Some people will be unhappy, sure, but at the same time, the burst of spending is good for the economy, will create jobs, etc., so I think the danger tends to be exaggerated by the people likely to lose the most (the rentier class and those who believe they are in it).