Instead of using wires to transport electricity, maybe we could transport the storage medium itself. 

Charged batteries or capacitors are moved from one place to the other, such as suspended in water streams through a network of pipes, or by trains or trucks. I've always though of these batteries as spherical for some reason. 

Would there be any advantage in this? Reduced power losses? More bulk energy transport? How to extract the energy efficiently?

One of the branches of this idea is for an electric vehicle. It would have a tank. We would refil the tank at the gas station with a load of these batteries or capacitors, This would be with mass transfer, instead of charging stationary batteries in the vehicle. Just dump the batteries inside the car as fast as possible. The idea is that transfering a batch of material is faster than charging batteries. 

I was amazed when I first learned how long it takes to charge electric vehicles. To this day, I can't tell exactly why does it takes so long to charge a battery.