Most people do have a desktop. They've invested years of time learning Windows and have applications specifically written for it. Desktop Linux has been around for years and hasn't made a dent in Windows. Why would a new desktop Linux distribution change that?
In many ways Android Desktop would be inferior to most desktop Linux distributions because it would be launching with few, if any, apps. Android has many mobile apps, but just like iOS and OS X, we would really need separate apps for both. Google could provide a Linux with Android APIs just as Apple shares much of Cocoa between iOS and OS X. However, traditional linux distributions are quite usable (my complaints about Gnome 3 and Unity aside) and they haven't made much of a dent in Windows. If people don't want those, why would they want Desktop Android?
Branding might help. People might hear Android and think, "oh, I've heard of that or used that before". Still, the "Windows" brand hasn't been helping Microsoft counter Google and Apple in the mobile space. In fact, looking at the mobile space, we can see how important inertia is. Despite coming out with a quite good mobile OS and getting Nokia to commit to exclusivity, that combined force just can't make a dent in consumer inertia toward iOS and Android. Even if Google came out with a premium desktop OS with the Android brand that people know and love, would users change their inertia?
It just seems less likely to me. In mobile, Google and Apple weren't fighting inertia. They were creating a new space.