There's nothing stopping anyone from publishing a primarily text-based site if they want, or an "app" site. The web isn't a zero-sum platform, there's room for everything, and no objective definition of what separates "documents" from "apps" to base such a division on to begin with.
No one wants the web to be forked except for people on HN who wish everything done with it since the 1990s could be sent into quarantine where they can't see it, but this isn't something the public wants, or that anyone is working towards.
The problem with adoption of the text only standard would probably be that the generic browser will support that use case just as well as the simple browser. In general it would be hard to choose between one or the other world.
Rather than that, how about offering a very simple CSS on top of RSS? So that feeds could be personalized a bit, should the clients choose to support this?
Simultaneously, blacklists of domains and browser extensions to scrub viewed pages of any references to sites not subscribing to particular philosophies.
The WWW will become the world wide app server. Focusing heavily on an app like experience.
Then there will be a push for a text only implementation to bring back the good ol' days when people actually want to read something on the internet treating it more like a book.