My understanding is that it is beneficial for the nations that export to the United States to buy US Treasuries as it keeps demand for the dollar high, which maintains the US dollar as a strong currency - meaning that a dollar has a high purchasing power. The strong US dollar compared to the currencies of exporting nations allows the exporting nations to remain competitive.
Here is my rough understanding of the process. It may not be completely correct though as I'm still trying to figure out all this alchemy...
Typically if a nation, let's call it Exportia, exports more than it imports (trade surplus) the demand for its currency increases (directly or indirectly) and that causes its currency to appreciate. Exportia's currency becomes stronger which means it has more purchasing power. And because it is stronger and can purchase more, it may require more of another nation's currency to be exchanged to get Exportia's currency.
So if another nation, let's call it Importia, wants to import Exportia's goods, and if Exportia's currency is stronger than Importia's, then it will require a higher volume of Importia's currency to be converted into Exportia's currency in order for Imprortia buy Exportia's goods (i.e. in order for Importia to import the exports from Exportia). This means that the prices of goods from Exportia that Importia imports will be expensive when priced in Importia's currency.
As Exportia exports more and more and it's trade surplus grows, its currency appreciates, and from the perspective of other nations like Importia they find these exports from Exportia to be more expensive with time. So over time Exportia's products become less competitive to nations like Importia. Importia find that it require more and more of its own weak currency to exchange for Exportia's strong currency in order for Importia to import Exportias goods.
The opposite logic holds for Importia's currency. As it imports more than it exports, there isn't strong demand for its currency. So it's currency is weak. While it takes more and more of Importia's currency to be converted to Exportia's currency, it doesn't take much of Exportia's steonger currency to be converted to Importia's weaker currency. So from the perspective of Exportia, products from Importia would be cheap.
So the general rule: an exporting nation tends to have an appreciating currency which would tend to make its exports less competitive with time. An importing nation tends to have a deprecating currency which makes its exports more competitive with time. At least that's the textbook theory... reality doesnt always work this way.
If the United States were like any other country with a deficit (importing more than it exports) then it would behave like Importia. Over time it's currency would devalue and it would find imports from the rest of the world growing more expensive while it's own exports to the world would become more competitive than goods from nations with stronger currencies.
If you are a nation that is exporting to the United States, say you are Exportia, then you will find that over time your exports will grow less competitive as the United States' dollar weakens and yours stengthens...
... but you have a way out. Buy US Treasuries. Keep it functioning as the reserve currency. It keeps the demand for the dollar high, which stops it from appreciating. This keeps the dollar strong compared to your (Exportia's) currency, and so your exports remain competitive and America's exports are too expensive to compete with yours.
Here is Hudson in a recent interview:
You’ll pay dollars to an exporter, from China or Germany — when there was still a German industry — and they turn the dollars over to their central bank, and the central bank would then say, “What are we going to do with these dollars? If we don’t send them back to the United States, our currency is going to go up against the dollar, and that is going to make our exports less competitive. So we have to keep our currency, our exchange rate, down; and we do that by buying Treasury securities”.