I thought that was to keep the electronics powered up. The 12V battery isn't enough to sustain them for too long.

A combination of both, I'd imagine.

In my experience (with cars, motorcycles and small boats), once a vehicle is started it tends to stay running.

That's my experience too. Maybe it's a chicken-or-egg problem.

The electronics and lights would certainly drain the battery, but the specific fear was that the car wouldn't start when needed. It was never specified whether that fear was of a dead battery or failed starter, but frequent starts and short trips will deplete the battery in any car...