That's true for class 2 appliances (two core, no earth required) because there's no chance of one of the conductors from coming in contact with earth, the only risk of short circuit between the conductors.
It is for the safety of the user. The fuse protects the cables from overheating and catching fire.
Yes, 'FIRE SAFETY' not electrical safety - so from that point of view, the neutral is just as good as the live.
For a class 3 appliances it makes a huge difference. The fuse must always be in the live conductor otherwise there's little point in having it.
What's a 'class 3' appliance?.