The web should be a method of delivering documents exclusively, and be limited to the kinds of things you can do with other computerized documents (the basics, but also Audio, Video, Animations, hyperlinking, etc.)
I'd be okay with locking these heavily-abused features behind a "web app mode" that the user has to enable on a per-site basis. It should include a restriction forcing all content to come from the same origin, so that the browser in that mode won't make it easy for web apps to include third-party tracking or advertising.