However, would it be possible to have a secondary transponder on board which would be automatically activated in the event that the primary was switched off?
jug: some pages back, a 777 operator indicated 777's have two transponders. Switching from one to the other pretty easy.
This makes sense, having two transponders as a measure of redundancy. Large airliners travel in dense traffic control areas in the departure and arrival phases of flight. Having the transponder working so that ATC knows who you are, and where you are, is to me a critical requirement, both for safety and for timely arrivals and sequencing.