"Library classification" peaks around 1960, and drops off rapidly. (The chart ends at 2000.)
Faceted classification has a meteoric rise around the 1960's, but falls abruptly from 1970 to 1980. The rise possibly corresponds closely to the activities of the Classification Research Group, based in the UK, whose big interest was in faceted classification.
This is hardly a scientific study, but it illustrates what my gut was telling me, which was that keyword searching has essentially replaced any kind of classed access. That does make me wonder what is being discussed under the rubric of "knowledge organization." Keyword indexing, per se, does not do any organization of knowledge; there are no classes or categories, no broader concepts or narrower concepts, no direction toward similar topics. It also has no facets, at least none based on the topic of the resource, only on its descriptive properties (date of publication, format, domain).
Keyword searching is not organized knowledge. Any topical organization takes place after retrieval by the searcher, who must look through the retrievals and select those that are relevant. This in part explains why Wikipedia is the perfect complement to keyword searches: Wikipedia is organized knowledge. A keyword search can pull up a Wikipedia page that will provide context, disambiguation, and pointers to related topics. I find increasingly that I begin my searches in Wikipedia when my searches are topical, leaving Google to function as my "internet phone book" when I need to find a specific person, company, product or document.
It makes sense for us to ask now: is there any reason (other than shelf placement) to continue library classification practices? Keep your eyes on this space for more about that.
Added note: Richard Urban offers this nGram view comparing all of the library classification phrases with the term "Ontologies":