Sort of like the difference between a CS major and a software engineer. One of my managers had taught English in school for many years. I agree that everyone in the group needs to enhance their communication skills, but I think the tech writer should be able to help them figure out how to do that, especially when the communication is written or on-line. In most organizations, too much and too little is expected of the tech writers. My personal goal is to make every software engineer I work with forever unsatisfied to have to go without tech writing support on any future projects.
Tech writing is like software engineering is a lot of ways.
For instance, one of the best kept secrets is that there is a tech writing process. I think the tech writer is especially useful in setting writing standards for everybody to get consistancy between documents. That is not easy. If that is your goal, it may take only one well written document to achieve it. Or, it could be one well written document followed by one poorly written one to show the obvious contrast.