Cannot install or move Android Apps to SD Card - is it a flaw from the Android or from the phone manufacturer?
Android supports moving apps to the SD card since version 2.2 (only for apps which allow it); however, this feature can be disabled when building the ROM. Apparently Samsung decided that about 9 GB of user-accessible internal memory should be enough for apps, and disabled the “move to SD” function in their stock ROMs for the 16 GB Galaxy S4 model.

However, there are recent news that Samsung heard complaints of 16 GB Galaxy S4 users and enabled the “move to SD” function in a software update.