I think this discussion applies to any of the arts. A painter can be taught technique, but another painter learns it by studying the work of others, while yet another simply puts paint to canvas. It is similar with music. In each of these areas, one can certainly point to specific techniques--how to hold a pencil for sketching, color theory, grammar, scales or tuning--that will at least expand the toolkit of the artist, if not result in actual improvement. At the same time, the mantra for each endeavor is practice, practice, practice. It's how we get to Carnegie Hall.
That said, there's something to compiling a list of techniques any of us have found useful. I gave mine, pedestrian as it is: show your work to others and get good feedback. Learn from that. I mentioned that one important lesson to learn from that process is to grow a thick skin, to learn how to take criticism. Indeed, some writers learn they *can't* take harsh criticism, which should be a warning sign, though not all heed it.
I do think learning the rules of grammar is worthwhile--one of the great boons of having learned Latin is learning grammar that I never learned in *ahem* grammar school. Here are some others that come to mind. In each case, one learns the rule in part to know when to break it. I would argue that both knowing rules and knowing how to break them does lead to better writing.
How to punctuate dialog
Standard use of dialog tags
Paragraphing
The basics of story structure (three acts, Hero's Journey, that sort of thing)
The vocabulary of fiction writing (e.g., beats, MRU, Mary Sue, all our goofy jargon). This doesn't lead directly to improvement, but it facilitates reading the literature of our craft
The tropes of a genre
I'm sure there's more. Has anyone looked at the syllabi of writing classes? Those might provide additional ideas.