Foreign countries buy USD through trade. Japan needs dollars for international trade so the US Treasury prints dollars and gives them to Japan and in return Japan gives the US Nintendo Switches or whatever. Those dollars go into the international trade system and some of those dollars will just circulate internationally indefinitely and won't ever make their way back to the US, hence the perpetual trade deficit. This is a great deal for the US because at the national level they effectively got those Nintendo Switches for free.
That’s not how that works. If Japan needs USD it goes to the forex market. That market represents a massive trade flow.
It doesn’t matter which currency you pick in that world apart from capital control. As long as it’s reasonably stable you flow through it with many billions of dollars a day with ease. The conversions are effectively free because the spreads are tiny.
Using the US dollar to trade between two countries that are not to US does nothing to the the currency. It just shifts a deficit.
The umbrella could already be gone. There are big question marks over how much the in-practice umbrella looks like the Ukraine war where the US State Department provokes something then Japan gets flattened in the crossfire. How much should they be paying for that?
People are coming out of the 90s mindset where the US was substantially more important than its competitors. It was easily worth paying for US protection then because it was obvious the US could back it up with muscle. Now the calculation is a lot less clear.
This is "broken window fallacy"[1] territory. In economic terms defense spending is mostly waste because a lot of it doesn't get used (hopefully) or gets used to blow other stuff up causing net damage. The fact that it creates jobs is better than nothing, but spending the same money on infrastructure would increase the future productivity of the country.
The defense budget is a social support program that conservatives will agree to. Rather than just providing people a basic income and healthcare directly, they add the hoop of holding down a job to access it.
It also is meant to keep American industry active (to some degree) in case it is needed.
No one else can project conventional military force anywhere on the global like the US. China is getting there but not quite yet. India and Russia are still regional.
The Europeans couldn't deal with a few land pirates practically in their backyard.
If the US has convinced itself that able-bodied young men who are good at following orders are the people who need social support then it is quite a bit worse than mere waste. That is $800 billion spent keeping the US's best labour out of the labour force.
The US isn't sending sad cases over to Japan to cash welfare checks.