Well, i guess certain people forget Ohms law with power losses. But you can better have a fuse in front of the mains than in front of your battery. Assuming the fuse has the same resistance P=I^2*R.
The current on the mains side is much lower, therefore the losses are much lower.
This is the same reason why working on a 115Vac mains voltage is resulting in much more losses (or thicker copper wires).
![Face Palm :palm:](https://www.eevblog.com/forum/Smileys/default/facepalm.gif)
Overall, relatively speaking for just the battery power supply, it's a little far fetched. Maybe you safe 1-2% at most. Really something that keeps you awake all night.