- I'd have to set up the WP instance and maintain it. I'd have to manage the account(s) on it. I'd have to manage the plugins and all of the sundry parts of running a web service.

- The WYSIWYG editor isn't as good as GDocs (or Word, or insert other popular apps)

- Collaborative authoring is a pain. GDocs has this built in, via accounts everyone already has.

The utility of ease of use/low-friction/lightweight-ness can't be overstated. Getting rid of even a small amount of friction from systems often pays itself back exponentially.

Now you have to set up accounts and manage wordpress versus sharing a google doc or something similar.

I dont really like using WP. Lots of alternatives out there that do great stuff.