I do agree that writing is not _necessary_ to improve your thinking. However, I think that writing about a topic will often if not always improve your understanding of that topic as well as your ability to communicate it. I think that's because when writing about something you have to be slower, more deliberate and more structured than thinking about something in your head which helps you identify gaps in your understanding which you can easily miss when the idea is in your head.

I think the better way overall though is just to try different methods of thinking and do what works for you. I also think more than one method is almost always better than just using one.