Of course stiffness helps power transfer. If nothing else, then it is because the load path is shortest with a stiff frame, and the shortest load path is the most efficient as a first principle.

One thing to ponder when people start trying to reason their way around the need for frame stiffness... in a "whippy" frame, there is no reason why all that energy stored in the frame (by bending it) has to come out of the frame to the road. There are a myriad of loss mechanisms once you start lengthening the load path, not the least of which are in the legs themselves by affecting the pedaling motion (feedback). In a flexy frame of carbon fiber, it might be worse as it is likely the energy is absorbed in the frame material itself (ever wonder why carbon frames "dampen" vibrations? That's the frame absorbing energy).