The risk of fire is very low with the engine running or not. Slightly higher with the engine running, but not much.

I would imagine that the biggest reason is that it's simply bad practice to leave any machine on when you're away from the controls. A kid could knock the gear shift. A crook could jump in. Let your imagination run wild. Any manner of remote but real possibilities can be avoided by simply turning the thing off. Kind of like wearing a seatbelt. Most people never need it, but that one time they do makes all the difference...