It's not really about 'writing skills', it's 'communication skills'. 'Writing' usually implies the ability to be creatively articulate, for example, like writing a long form news article. People can be great writers and poor communicators. For coherent team communications you even don't need proper grammar - what you need the ability to be clear, succinct, appropriate, provide context, timely etc.. It's not about 'wr…
On the other hand I consider myself a good communicator, I can type a succinct email with a clear structure, I can create a damn fine Wiki page with indexes and all and I also communicate pretty well over text-based chats (started with IRC in the 90's).
Still, I couldn't write a 10 page report to save my life (still have one due for a course, been putting it off for 6 months now...)