Re: FirefoxOS?
I seem to remember coming across a few embedded type distributions that allowed you to set them up in a "kiosk" mode, effectively running a copy of Firefox and little else. Alpine for example can be set up with effectively no pre-installed software beyond the basic desktop environment, and a copy of Firefox added.
Very lightweight and quite usable even on 15+ year old hardware although its not the friendliest to use if you don't have much experience with the terminal etc.
To be honest, though...its not likely the desktop or distribution that is the issue, more the bloat of modern web browsers and indeed the modern internet. If it struggles with an up-to-date desktop, it won't cope with modern web browsing well at all.
The weakest computer I own is a 18 year old Netbook with a single-core Atom processor, giving it performance akin to that of something like an early Pentium 4. It'll run a lightweight desktop environment like XFCE just fine, but modern Firefox or Chromium are both very heavy on such a low-power device. Anything beyond a basic website is very sluggish and awkward to both load and navigate.
Equally I wonder how good Google's support will be for some of the more niche hardware configurations out there on Chromebooks. The very low end ARM powered ones with tiny eMMC flash storage likely won't take to Googlebook OS (what a stupid name) well, assuming they can run it at all or the hardware support exists.