Documents should offer the same granularity.
That neither content creators nor browser vendors are particularly concerned with the production and consumption of documents, as such, is precisely the issue. This is evident in the banner that the majority of the work has occurred under over the last 10+ years: they're the Web Hypertext Applications Technology Working Group.
No one, not even the most well-intentioned (such as the folks at Automattic who are responsible for the blogging software that made Christina's post here possible), see documents when they think of the Web. No, everything is an app—take this page, for example; even the "pages" that WordPress produces are facets of an application. Granted, it's an application meant for reading the written word (and meant for occasionally writing it), but make no mistake, it's an application first, and a "document" only by happenstance (i.e. the absence of any realistic alternative to HTML & co for application delivery).