The number of people in this thread breezily dismissing the value of effective writing is taking my breath away. I don't think these confident declarations we're getting in this thread paint a remotely accurate portrayal of skills that actually help career advancement. I think everyone's kind of playing a game where it's treated as a trick question and they're looking to emphasize the exceptions as much as possible.
Any sort of work, in say, nonprofits, or public relations, or marketing, or consulting, or any institution where you're at a level of management where your job is to present plans and preside over their progress while being accountable to oversight, and these are examples of the top of my head where I have at least some sort of familiarity, are places where strong writing is an asset. And I'm sure I'm just pointing to a small slice that I know from my own experience. These aren't special exceptions. These are the norm. The counterexamples make me wonder what, if any, actual career experience people are actually drawing from to claim otherwise, or whether they have the perspective to understand how representative those counter-examples actually are.