Yes, the Fredonian government is going to end up running a deficit not just because interest rates will be lower, but also to make up for the loss of income as a result of the current account balance. Importing decreases income and exporting increases income, which is why GDP includes a trade term of exports-imports. In the US, these are all the people who drop out of the labor market or go on disability as a result of being displaced by foreign imports, creating a loss of the taxpayer base and an increase in benefit payments. Thus imports are a drag on the fiscal balance as well.
This is the same reason why a policy of "inflating the currency" is not going to work for the US, and instead capital controls are the policy option of choice. I don't want to get the goldbugs in this thread, but the quantity of money is demand determined by the private sector, and the policy variable that the government has is the overnight interest rate. This means that "inflating the currency", or trying to create inflation, is done by lowering the policy rate. Fighting inflation consists of raising this rate. So when you say "inflate the currency", what you mean is lower the rate of interest. But that rate can only be lowered to zero, and more importantly other nations will respond by lowering their interest rates. This process is called "competitive devaluation", because what matters for the trade balance is the relative value of the dollar with other currencies, not the absolute value. The US cannot unilaterally set the relative value, and devaluation by US will be met with devaluation by our trading partners.
Moreover devaluation is very risky and might substantially increase the trade deficit, because when the rest of the world devalues their currency to match, it is much more likely that they are the ones who will suffer a currency crisis than the US. So this policy would risk destabilizing the currencies of our trading partners, leading to financial crisis and another flight to the USD as a safe haven as investors flee the currencies of our trading partners and rush to the US.
On the other hand capital controls is something that can be done unilaterally and cannot be countered in the same way as competitive devaluation. If we impose a tax, of say, 2% on foreign holders of US assets, and the rest of the world retaliates with their own tax, then this is unlikely to cause a global currency crisis, it will cause cross border capital flows to suddenly reverse in which US investors pull their money out of foreign nations while foreign investors pull their money out of the US and bring it back home. Because foreigners invested more in the US than the other way around, this should result in more capital flowing into the rest of the world rather than the kind of capital flight that creates a currency crisis.
In terms of how we got to this point, that's a tough question because you are asking me to assert motives and plans, when all I can reliably do is describe the current situation we are in. If I were to guess, I think it was not intentional. When the UK was the dominant economic power and the pound was the reserve currency the UK also suffered from chronic trade deficits, but the size of the imbalances were so much smaller before WW1 than today. What is happening now is truly unprecedented in the economic history of the world -- the depth of global supply chains, and the size of global trade imbalances is not something anyone would have predicted. So my guess is that the US maintained open capital markets for political and historical reasons -- because England did, and because market liberalism was a dominant economic philosophy. The US maintained rule of law for similar cultural and historical reasons. Then, after WW2, ours was by far the dominant economy, and everyone wanted to invest their assets in the US, particularly when the rest of the world was in shambles after WW2. It's said that the Marshall plan -- that transfer of dollars to Europe -- only partially offset the flight of money from Europe to the US as people wanted to invest in our bonds because we were a safe haven. So I would say that's how we became a reserve currency.
But in the beginning, the amounts were so small relative to the size of our economy that it didn't disrupt anything.
Over time, it did begin to disrupt things, but perhaps the benefits outweighed the costs to the people who mattered. Those working in US capital markets benefit from this system, since they get a cut of the transactions. And there is still a contingent of die hard market liberals who insist that we must maintain open capital markets, even as the rest of the world takes advantage of this.
Then businesses benefit, in the short term, from outsourcing. Consumers benefit, to some degree, from cheaper imports. The lower interest rates cause asset prices to be higher, so houses are more expensive as are stocks. This benefits the generation that bought the assets when they were cheaper.
So it's not the case that the entire nation is a loser. There are constituencies that benefit from this system and they have power. However the costs are mounting, and the benefits are fading. It's great to have a huge increase in house prices, but that's a one time hit -- a transfer to one or two generations. For the generations that come after, housing is just more expensive. It's great to have boosted stock prices from outsourcing, but now US firms are discovering that they have foreign competitors who are climbing the value the chain.
And of course the social costs for working class Americans are devastating, leading to political instability. I think we are well past the point where the benefits outweigh the costs.
By the way, I am not predicting that we adopt capital controls -- such a thing would be unheard of for us, since we are so indoctrinated in believing that free flow of capital is a type of virtue. However I am a believer in the principle that unsustainable things at some point must end. We cannot continue to bear this burden indefinitely.