Re - Parachutists and plastic planes - you still have the problem of a ground plane for the antenna and the fried nadgers issue.
I think you will find that the 250W reply transmitter is on for about 1.6% of time the transponder is actually being interrogated. Assuming the SSR beam width is 3-4 degrees, a given ground station will illuminate a transponder for about 1% of the time. Therefore the 250W output is only needed for about 0.016% of the time, and is therefore a vanishingly small amount of the power requirement.