This technique is used to prevent shock hazard in electric devices connected with unpolarised AC power plugs and sockets.
Double switching is a crucial safety engineering practice in railway signalling, wherein it is used to ensure that a single false feed of current to a relay is unlikely to cause a wrong-side failure.
A similar accident on the United Airlines Flight 811 was caused in part by a single-switched safety circuit for the baggage door mechanism.
Failure of the wiring insulation in that circuit allowed the baggage door to be unlocked by a false feed, leading to a catastrophic de-pressurisation, and the deaths of nine passengers.
On the other hand double switching is inherently less prone to wrong side failures; it helps overcome short-circuit faults that are hard to test for.