They are great writers if you tell them what you want. If you're unable to properly articulate the writing style you would like as you would a software spec, well, garbage in, garbage out.
So it's not a matter of inability but rather awareness and know-how.
Then secondly, humans learn to write intuitively and heuristically (for example "paragraphs should align sentence subjects with an identifiable flow of conceptual main characters/actors" is an entire chapter of expert writing advice traditionally taught at the undergrad level). The act and teaching the act are different beasts. The way to specify would have no objective, clear best practice to do so: Even an English teacher or a language expert would be challenged to come up with a concise list of instructions to set up an LLM to output something of sufficient quality.
I’ve been experimenting with having LLMs write/update academic notebooks for me, and so far the best results I’ve gotten came from correcting their output and asking them what they’ve “learned” from my feedback.
Give it some paragraphs of writing you like, authors, writers, whatever. Also don't expect to one shot long papers. Have it write out a table of contents and write it in small chunks.
Typical things I'll say is avoid purple prose, avoid common cliches and tropes, "show don't tell", avoid wild metaphors and similes, etc. But it all depends on what you like. Look at things you do like and try to think about what it is about that writing that is different than a middle schooler or an AI writing it. Theres no formula for it.
For me, my amateur attempt is having another LLM do a review loop to remove clearly offending phrases and a heuristic eval to change sentence structures to be more similar to mine, THEN my manual HITL loop to rewrite ~20% of the sentences anyway.