No links, no bookmarks, no standard UI conventions and components, no history, no back and forward buttons that work consistently, no mental model of how it all clicks together (page model), no accessibility, no search, no semantic content, no pesky users controlling stuff. Sounds awesome, sign me up.
Sarcasm aside, we're moving in that direction already.
Yes! How I longed for the days where scraping would be impossible, locking us out of many innovative interfaces and mashups (or even just archiving pages, like e.g. Pinboard does). Where Reddit's Enhancement Suite or the many Hacker News bookmarklets and greasemonkey scripts would be impossible. Where I can't just copy a piece of HTML to my clipboard, just dumb images.
I recommend checking out Section 4 of the linked technical report, which discusses how to recover traditional interface elements of the traditional web.
Wow, an entire other myriad of issues I wasn't even thinking about while commenting. Great points! Funnily enough, you can see some of this in mobile apps already, but it's gotten a lot better over the last 5 years. No search really bugs the crap out of me. It's impossible to naturally discover an app through search. Also, It's like mobile apps are all their own individual walled gardens and interplay is impossible. Links anyone? All this was invented years ago and seems like a step back.
But this wouldn't even have, like, font rendering. Input methods. The amount of stuff every single site would have to implement just to show something on the screen is staggering, unless the API in question is no longer small and simple and provably safe.
You don't need to reimplement it, you just use whatever library you were using before (but linked with the browser). The point is that the stack doesn't change, just who provides it.
Sarcasm aside, we're moving in that direction already.