The idea behind categories on Wikipedia articles is that readers and editors will be able to use category pages to find encyclopedia articles that interest them. Every time we talk about a category-related project, I wonder: Do normal, non-editing readers actually use those to find Wikipedia articles?
My current feeling is that they (mostly) don't. They're not visible on mobile, but I've never seen any complaints about them being inaccessible there; if they were widely used, then someone would have complained about the loss of functionality.
It should be possible to use page views for the content categories (excluding hidden/maintenance categories), and comparing expected vs actual page views for logged-in and logged-out users to come up with an approximate answer to my question.