"What makes them [China etc.] invest in the USA? It seems to me that it comes down to faith in the US Empire, past and present (past faith is important, too, because of high costs of transition for countries like Japan and China that have accumulated lots of dollar reserves), and absence of an alternative."
Absence of an alternative is most to the point. If China did not extend credit to the US, the US would not be able to buy back China's goods. It was the same relationship that Japan had with the US in the eighties, or indeed that the US had with Europe throughout much of the twentieth century. On any model of capitalism it is always worth remembering that it has to perform as a distribution of goods to function. But this is to fix on the most superficial aspects. The essence of America's credit rating is the prospect that they will continue to generate wealth out of the phenomenally large labour force that is put to work there every day; just as the essence of China's output is the exploitation of its own workforce.
If anything, the recent record of US militarism would tend to undermine rather than reinforce its credibility, and bad news in Iraq often corresponds to poor NYSE performance.