I would like that kind of distinction to be made too somehow for battery life and security/privacy reasons.
I suppose your concept is partially implemented by the "Reader" mode that Safari introduced which I took was an attempt at "zen-ifying" the browser.
I think Reader Mode is largely a flop because 1) it is confusing in that it isn't always on offer by the browser/is context sensitive, which seems like an odd choice, and 2) some pages don't/can't always render sensibly in reader mode for absolute positioning/layout reasons.
My solution to this problem is to give content creators and web application developers better tools to separate between the "page" and "application" use cases.
For "page" content creators, it would be great if they had a framework that poured their content into the browser in an automatically screen-reader accessible way AND was formatted prettily. It's my personal theory that an optimally readable site also happens to read well to a screen-reader, so we can kill two birds with one stone if we abstract the content delivery a bit and force it to be rendered accessibly.
For "application" developers, it would be good to have the framework provide more/better standardized widgets than what the stock HTML5 offers. I'm thinking twisty trees, multi-select lists, streaming infinite scrolls tied to data sources, etc. These widgets would be screen-reader accessible and standard hotkey-enabled where the hotkeys would function the same from site-to-site (mandated by ToS or license).
Finally, the "application" side of this framework would include widgets to display inline "page" content where the user could toggle the "page" content to go full window or full screen and provide that zen reading experience.