On the other hand, many of the pages that saw a decline don't have any search snippets based on the Knowledge Graph, and therefore the decline for those pages cannot be explained this way.

Yes it can. Knowledge graph leads to less traffic at pages that have snippets, leads to less people clicking on to pages that don't.

Because even the simplest query for someone's birth date, the kind that the knowledge graph snippet can intercept, will sometimes lead into a night-long wiki binge.