I first thought it was because of World War II propaganda, but on further reflection I don't think that's right, because (1) the propaganda more often used the

I first thought it was because of World War II propaganda, but on further reflection I don't think that's right, because (1) the propaganda more often used the slang "Japs", and (2) I think "a Japanese" and "a Chinese" were both common in American English for decades after the end of the war (and the American war propaganda was never directed against the Chinese). I think I favor the theory that someone else suggested in the comments here that the Japanese and Chinese were the only East Asians that most Americans were aware of in the past, and were subject to a lot of hostility and prejudice (both before and after the war), and that people at some point felt that the singular noun forms had acquired a possible interpretation as slurs because of the memory of this. That matches my understanding of "a Jew", which of course is the perfectly normal and traditional form in English, but which many non-Jews and plenty of Jews have become uncomfortable with as a singular noun.