While Android is based upon Linux and could technically be run on a PC, the user experience would be horrible. They couldn't even get a good experience on tablets, which have much more similarities to phones than a PC.
ChromeOS is Google's current "desktop" offering, which allows you to run Android apps. This is pretty much the best you'll get now. Emulating the app environment means that app developers don't have to code specifically for the myriad of possible PC displays; this already sucks for the numerous phone resolutions.