Word documents have extensive markup and revision tracking features, and then they're passed around within emails that function similarly to commits. Git is only really useful when you're doing simultaneous changes to a large number of files.
I don't think standard git with MS Word blobs would be better though.
What I would like would be the conceptual structure of a git version history but with a commit viewer that could represent the commits in Word's revision control style as well as pull requests to track incremental agreements to change the document.