Before that was a neat Linux project Pyrodesktop (2007) which was an x11 window manager using Firefox guts to render. There was also a trend of trying to mate Javascript technologies to gnome back then, with efforts like gjs seeing some adoption. I don't know how popular it is, but a spinoff of css was/is used for styling in GNOME for a while.
These days there's tons of web desktop projects. https://github.com/syxanash/awesome-web-desktops . Only sort of in the spirit but i quite adore Greenfield, an html5 Wayland desktop/compositor. https://github.com/udevbe/greenfield
I absolutely think there is all-in potential for the web. I think we're missing a visible rallying point, where a stronger community of app makers can cooperatively advance beyond-the-web capabilities. Project Fugu & WICG help a lot but are also working with Safari (and sort of Firefox) handcuffed to them.
You may be thinking of Palm webOS which failed in the market, partly because it felt slower than Android, iirc.