Here are a few highlights, including a definition of written language, from Ch. 1 of Vachek, Josef. 1973. Written Language: General Problems and Problems of English. The Hague: Mouton.
In Ch. 1, The Pre-Functionalist Views of Written Language, Vachek defines written language, tentatively, as "the system of grammatical means employed for the purpose of producing written utterances acceptable in the given language community." p. 9.
Vachek speaks of a system: Each grapheme, or typographical mark, "belonging to that system is mainly characterized by being different from the other graphemes of that system." p. 9. "At the same time, the rules governing the use of these graphemes ... have a clearly normative character ... and any use contrary to these rules is felt as contrary to the norm" and evaluated as a mistake or deliberate variation. p. 9.
And the Baudouin de Courtenay 1881 remarks are remarkable for considering "written utterances as structures of their own kind." p. 12.
Indeed: A productive course of research into how writing can better be taught might be to consider the structure of texts.
Vachek's Functionalist Approach to Written Language
The Three Topical Progressions
How to Diagram Topical Progressions