eh, I own an Acer Chromebook R11 and am pretty happy with it...

The battery life is wonderful for that price bracket (~8-10 hours, <300€). I used crouton for a few month, which enabled me to install Ubuntu 14.04 in dual-boot. you could switch between ChromeOS and the chosen Linux window manager (i first used unity but switched to i3wm eventually).

At some point, i removed it again because I hardly used the Linux environment anymore. There a pretty fine text editors as offline chrome-extensions available (i.e. Caret) and that was the only two use-cases I had for the laptop... browsing the internet and making text notes.

BTW, a lot of webapps, or "Web browser app" as you call them, have offline support. So no, you don't need an internet connection to use them.