It’s easy to say “this is a writing job” when the title is “writer,” but many more jobs are primarily about writing. These days, many “journalists” are writers who rely on published accounts to rewrite stories (and hello, fellow bloggers!), and “social media manager” probably involves a lot of writing as well. It’s hard to communicate well in a noisy and crowded field.
In addition to these “you are a writer!” jobs, many others also require writing as a primary ability. This includes people-type jobs (e.g., business management) and technical jobs (e.g., engineer). The type of writing done for such jobs may be highly specialized, but those who can write better will be better at them.
For some jobs, it’s clear that some skill has to be developed first: I’d rather have a surgeon who is great at surgery and mediocre at writing than the reverse. For other jobs, writing is so fundamental to the job that I think (in my entirely not-self-interested way) that companies should look at writing as a key job skill. A mediocre programmer who writes well can improve their programming skills, and probably will; a great hacker who writes poorly will continue to produce under-documented or undocumented code that will need to be rewritten by the next person to need changes.
There must be other examples, but pardon me while I go back to reading this undocumented code and trying to figure out why it’s misbehaving.