I really feel like the entire session model of the web needs reworking from the ground up. I honestly want most of the websites I use to act more like apps, with a dedicated space for that site and not spread out across N tabs or windows. And also containerized exactly like this describes.
There are some browser extensions that to do this, but they're pretty clunky overall.
In what I want I don't really see that being different. Not everything is an app, but the things that aren't are things that I don't visit every time I sit at a computer.
Mostly I see it actually working a lot like android's url-based intents, where there are things recognized as "apps" and actions directed at urls within that scope go to that 'app' to decide what to do with it, and things outside it go to a more traditional browser environment.
There are some browser extensions that to do this, but they're pretty clunky overall.