I guess the issue is that a modern web browser is a sandboxed application runtime which also happens to function as a document browser. It's been going in that direction for a long time (since webmail became common), and there are real advantages of the browser as a platform for applications - it's cross platform by default, and it has pretty good sandboxing.
So probably the most you can hope for is that we split the document part of the web from the application part, so that it's easier to make a viable document browser. But it's not clear what advantage this offers for anyone who's not trying to make their own browser. Security is probably much simpler for the document browser, but the logins and sensitive data you care about securing are probably in the application browser anyway. And we've spent the last 20 years blurring the lines between documents and applications (think of a Github issue page, for instance), so even if it was possible to access information as a pure document, there would be advantages to looking at it in an application browser.
