Random list:
Your input supply needs to be stronger, because it potentially has to charge the batter + run the device, that means a more expensive supply.
Extra circutry needed for supplying the device from either the battery or the fixed supply, this is not exactly hard to do, but it still means extra engineering, extra components and extra testing.
Thermal design can also become a problem when you're both charging batteries and passing current to the device.
Then there are safetey issues as detaro mentions
For some devices it's considered a safety feature. e.g. an electric razor that's advertised as watertight and usable in the shower, because then someone will try using it in the shower while plugged in, and that's not a safe idea. Also applies to some medical stuff.