Assembly to C is not the same thing as Unix to Chrome.
Your argument would work if, say, people start writing operating systems in Python.
Another important thing to realize: there's a big difference between the OS and the GUI. The GUI might very well be implemented on top of "web" technologies, but that's not enough to say that the OS is the browser.
Well, the portability improvement from Assembly to C is mirrored in browser applications compared to native one in my view. The Browser today abstract a lot of things for you now including network communications, device interaction, file system interactions, graphics... the list goes on.
These aren't all GUI related things. I strongly believe you can now have a OS that is basically booting you into a browser and all OS interaction would go through WebAPI and still build most applications we use today.Obviously there will always be cases which you need to drop down a level.
Developers of ChromeOS or boot to gecko seem to agree somewhat.
Windows 8 supports HTML/JS for creating apps using WinRT, but it's hardly usable in any web browser like Enyo apps are. Not to mention the ability for creating apps using .NET or C++ are still very much a possibility--perhaps even preferred.
Some people use to cling to assembly instead of using C. Now days it's rare to find someone who will use Assembly over C.