Chain and sprocket wear is probably proportional to chain tension, and chain tension in turn is the force you put into it while pedalling. Then again, the faster speed at which the chain moves internally and against the sprockets could also mean higher losses and greater wear. I'm not a drive train engineer...

Power is force*speed, so you can double the speed and halve the force and still put out the same power. That shift in the speed/force ratio is what you use gearing for.