The problem with "one client to rule them all" is a massive lost of consistency, speed/responsiveness, and usability when it comes to documents. On the web, documents can come in anything ranging from the form of a tiny text file to a gargantuan "app" that weighs tens of megabytes and spins up your laptop's fans to render. It also means that the browser isn't nearly as smart as it could be because it has to be a general purpose jack of all trades.

A dedicated document browser would likely almost always blazing fast, regardless of the machine it was run on and the network over which the documents were transferred over. It could have features that would make no sense in a web browser but greatly enhance the experience of reading and navigation. It could reasonably cache nearly everything the user visits (since it's practically all read-only and small) to reduce server load and increase speed. In a nutshell, it could be far better at specifically working with documents than a web browser ever could, even with a laundry list of extensions installed.

Additionally, it would actually be possible to write brand new competing document browsers due to the vastly more simple specification, which is something the web will probably never have again.