... or Linux desktop-on-Android

Both ways are worthwhile. Linux desktop-on-Android would seem very doable, either run Linux binaries (probably chroot'd as libc is different) with a rootless X Window System running on Android, or port GTK/Qt to Skia graphics; it's just tons of work either way.

You would think Google is figuring this out so Android and ChromeOS are cooperating runtimes on one kernel; a Chromebook capable of running a subset of Android apps (like Google TV) seems useful. But for whatever reason the two projects are disjoint and ChromeOS is resolutely web-centric. FWIW I've tried booting Android-X86 and it failed on desktop and laptop (as did Chromium OS), perhaps due to poorly-documented graphics requirements.