The title is self-explanatory, and I agree with the statement.
I’m still not a very good writer by any mean, but I agree that every software developer needs to improve their writing, both if they work in a team or they work alone.
I had this discussion with a friend not long time ago, and we imagined a completely remote company, without the possibility of using slack or any other synchronous tool (chat, video, calls, etc.), only asynchronous tools (email, documentation, pull requests, etc). If no one knows how to write well and how to explain complex concepts in short writing, there is no way this can work, but if everyone in the company knows how to write very well, this could be the ideal company, where everything is well documented, everything is written down and everything can be reviewed later and during any process you can go back in time reading exactly what you were writing before and how things evolved over time.
This is a very idealistic case, but this case shows how much power would be to be good at writing, and writing more than what you are used to doing in your day to day development job.