[dusted]

There are some complications to implementing a power supply that works both off of battery and from the input power as well.

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