I don't see that happening yet in the next generations. At least not, when such browsers don't offer you much more than just a plain viewport on whatever the front-most application is doing, and when applications and many mobile devices still don't have any clear, central, general, and personal area where to store stuff.
Users always want and need to integrate stuff with each other, and know where their stuff resides (even when it's just a virtual representation of a location). Browsers and many mobile systems and devices are not good at this, yet.
Users still have many difficulties with the mental system of using cloud based storage. It's not the idea of having something stored remotely, but having all these brands and types of cloud service suppliers, offering many but also very different kinds of interactions and collaborations.
So it's still too difficult to interact between their pretty looking viewports (and the applications behind them). Their content is still too separated, too unhinged. There's no system between these windows, overseeing and bridging their functionalities.
JavaScripts can be powerful, but they can't demand, become, or impose such an overall operating system behind the browser, offering a safe place to exchange and save stuff. That's a pity. We still need an OS...
Oorspronkelijk geplaatst op Quora: Is it possible that in the future your browser will be your de facto OS? Is it possible that there will be no difference between desktop apps, mobile apps and web apps? Don't you feel this trend to make everything on the web?"