I wonder why there are sites in which the reader mode is not even available. I can't think of any right now but it happens with relative frequency to be annoying.

Because Reader Mode is using heuristics to fetch the content of the article, and that can fail if the article is weirdly formatted in HTML. You can read more about this on the repo for Mozilla's Readability, which is what Firefox uses under the hood: https://github.com/mozilla/readability