Everything must be packed into 16 or 32 Mbytes of flash memory. In fact, you may have to slim down the OS so far that critical dependencies with other system components are broken, necessitating deeper changes to the architecture. Users have expectations of appliance performance, which stem from decades of using radios, televisions, etc. Waiting is not supposed to be part of the game, and appliances need to distinguish themselves from PCs in this key area. This becomes especially important for broadband-connected appliances, where multiple streams of simultaneous audio and video will be the norm rather than the exception.
Custom look and feel.
Appliance vendors want to deliver a product that looks like their own creation from top to bottom, not a warmed-over version of a familiar desktop environment. Vendors want their look and feel in every nook and cranny of the user experience, not that of the OS manufacturer.