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Now with a recent update to the Facebook for Android app, support for new devices has been quietly added.
You can now install Facebook Home on the Galaxy S4 and the Sony Xperia ZL by selecting the "Use Home Anyway" option, which frankly doesn't feel very convincing. Meanwhile the HTC One can install Facebook Home without the "Use Home Anyway" warning.
Facebook's focus has seemingly shifted to improving their Facebook Home app instead of updating it with new features. This could mainly be due to the negative reaction based on the 1 million total installations of the application.
Our own tests of a hacked version of Facebook Home on our Google Nexus 4 proved the app to be quite a battery hog, draining out batter in mere hours of use. The could be the reason it hasn't made its way across more handsets.
source - Android Central