Word processing still happens largely through desktop applications such as Microsoft Word, LibreOffice or Open Office. Google Docs is a great online alternative, but it's not open source, and documents are saved on outside servers, which can be a security issue.
Fidus Writer has been developed for a year and already has many of the same qualities as Google Docs -- the ability to share documents, to create Epub or HTML output, comments, powerful math/formula formatting and individual pages, Fidus Writer is also the only online tool designed for WYSIWYG collaboration on LaTeX format. Version 1.0 has been released and is functional. Try it
With sufficient funding, we could go ahead with these features. Everything will of course be published under the AGPL license as the current Fidus Writer already is.