Earlier quoted context omitted.
I'm not seeing anything anachronistic about either term. "Seasons" is absolutely aligned to the way television series are still produced and distributed. "Box Set" implies physical media. Using the latter term to refer to something else sounds like a case of false advertising.
With the advent of digital music, "record album" morphed from referring to the physical medium, to referring to the recording that would be put on it. I think something similar is happening for "box set".
The term "album" by itself did originally refer to something physical -- a collection of photos bound into a book by a glue made from egg whites ("albumen") -- but the semantic shift to "album" meaning any kind of collection offered as a single unit happened well before "record albums" were a thing.
But the term "box set" has not experienced a comparable semantic shift, and still implies the presence of an actual box.