Maybe we're talking at cross purposes; what I mean is that PCA+KNN or other tricks mean that for high dim and large amounts of data you can get useful results;

Maybe we're talking at cross purposes; what I mean is that PCA+KNN or other tricks mean that for high dim and large amounts of data you can get useful results; with the enlarged view of KNN as "anything where the last step is KNN" your statement that it's "astoundingly bad" is wrong. But for the narrow view of just KNN then sure cod applies.