Sometimes you are needed to maintain power supply for your device for some time when the main source fails. It can be alarm system or some light source or digital clock. Of course if source interrupts are very short, there can be capacitor with big capacity connected, but it is not reliable. Better use backup battery and diode.
This solution is very simple and cheap. The diode protects the back current float to battery. This doesn’t take much space to implement as the main bigger part is battery. As there just backup source it is not necessary to use rechargeable battery.