However, being an engineer, and writing in my engineering blog, I targeted mainly engineers.
But yeah, everyone will benefit from good writing skills.
Most of what you write will be skimmed or not read at all. The only way to increase your odds is to make your writing engaging (to improve chances of it being read) and clear and concise (to improve chances of comprehension).
Another oft overlooked skill is to know when to repeat your message in multiple places, and how to do so without it being irritating or noisy or irrelevant (see also: when not to write anything at all). Again, this increases the chance your message gets across.
Early in my career I took something that was technically complex for me, and wrote it up as a book, using the path that lead me to understanding it.
Assuming that some of my peers might benefit from what I learned, I "self published" (aka printed copies on demand on my newly bought double-sided printer) and sold it for $50. I sold about 1000 copies over the next few years.
The money wasn't earth-shattering, but the effect on my career was immense. I was the one who literally "wrote the book". As far as resumes go, it's pretty up there.
Part of the success (I think) was that it was specifically designed to be an easy read. The goal was to get to the end and "know" a bunch of stuff, without it ever being anything but obvious.
I think it was helped by understanding where my own mental blocks were, and by unpicking those blocks, allowed others to easily disassemble and pass them.
In my experience the biggest block to learning is in understanding that something we absolutely positively know to be true, is actually false. Without letting it go first your brain refuses to accept the new (however simple) because it clashes with what is "true". But that's a digression for another thread.
It's completely alien to me that people here seem to believe engineers should be spending time making requirements and architecture documents more engaging. You're paid to read the thing, just read it.
Your goal is to get your message across when your writing is skimmed.
That takes immense skill as a writer. Immense skill.
Paris Review is a great book to get an overview of mastering this skill.
A writer has to be interesting though, every piece of writing we consider well written has a quality of gripping the mind. I'd argue then, that politicians though they may not be in the habit of writing long academic style treatises or "interesting" articles, perhaps it can be argued in the past they largely did, still if they are in part elected on the basis of their speech, must possess the same ability in writing.
If you don't believe me then how is it that Trump's tweets are works of art, "I have never seen a think person drinking Diet Coke,"The Coca Cola company is not happy with me--that's okay, I'll still keep drinking that garbage.", etc... Crude, in bad taste, whatever you say. Another example is Obama, who honestly has a gift for writing in the conventional sense.
You can also have incredibly skilled orators where it’s all in the substance, but you can really only do that if you message actually has substance to it in the first place.
My own verbal and political skills aren't great. I am not a manager! Writing well has been good for me personally in terms of being able to organise my own thoughts better, and to be succinct in a way I can't when I speak.
I find my opinion is consulted frequently partly because I can summarise complex issues and present it in a way others can work with.
Senior engineers or architects may do more design than coding and the design needs to be conveyed likely as writing and hopefully a couple diagrams.
Managers absolutely need to be good writers to communicate effectively, advocate for their team, and tell the story of the team’s work.
If you’re an engineer and want to have a higher level job than you have now, getting better at writing is only going to help. I’m not saying it’s a MUST because I’m sure there’s some outliers, but it won’t hurt.