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.
Of course that umbrella could soon be gone, so it would be a moot point
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.
So it doesn't cost the US anything.
[1] https://en.m.wikipedia.org/wiki/Parable_of_the_broken_window
It also is meant to keep American industry active (to some degree) in case it is needed.
The Europeans couldn't deal with a few land pirates practically in their backyard.
The US isn't sending sad cases over to Japan to cash welfare checks.