Usually just if something rotates, to keep from accidentally unscrewing it self.
Left hand thread is more common than what we might imagine. Rotation is one of the main reasons as stated.
Fans are known to use left-hand retaining caps (nuts) so that the fan blade does not com loose when in use. Automotive have used right and left hand self adjusters on brake systems. Accidentally interchanging these will lead to brakes too tight on one side, and no action on the other side. Caliper pistons can thread in and out in opposite directions.
If anyone is old as me will remember working on a Valmobile with the infamous left-hand threaded flywheel nut. Miss observing this will usually end up in a broken crankshaft.
It is very common in mechanical watches to use left hand threads on the ratchet winding wheels, this is used so the wheel does not come off/loose during winding. Sometimes you will find that the pinion ratchet wheel is attached with a left hand screw, and the ratchet wheel mounted to the spring barrel is right-hand thread.
I am not sure why this was done, but I can see a benefit of when unscrewing a Gretsch knob, the retaining screw will assure that the retaining stud stays in the body. But the downside is if you tighten the knob too much, you can actually start to remove the stud.
The Schaller type retainer does not put a rotational force on the strap button/mounting screw. The collar rotate freely around the button. Those screws are right-hand thread.