The best example is trying to block a zerg early hatchery. Most pros will set their worker to patrol in a small area to block the hatchery. Why not hold position or just "stop"?
Yet another reason is that a patrolling worker will attack other workers that come near it (IIRC). An idle worker will just run away, which means they're no longer blocking. Whereas if they send a worker to build a building where your patrolling worker is, I believe your worker will attack theirs, and if they don't notice it, could even kill it.
Edit: As the comments indicate, I might not be right about workers attacking when set on patrol. I haven't tried it lately.