From my experience with iaido, sliding the foot along the ground is actually just the first level of a more complex skill which involves expanding your energy forward from the hips (and sliding the legs back involves compressing your energy). The movement actually comes from the hip and is expressed in the foot.
This changes rather drastically the power expressed through a technique like a two-handed sword cut or a throw.
With a rapier, the act of stepping actually allows you to, well, fall forward onto the foot you lifted, giving you greater and more sudden power in that direction as long as the movement is coordinated properly.
This is similar to trying to hit someone with your fist and bringing it crashing down with all your force on their collarbone -- or relaxing all your muscles and letting gravity do the work. It turns out gravity provides you much better acceleration than your muscles ever will, meaning that with the appropriate amount of skill, you can provide a very light, very quick touch/pierce with a rapier in a very particular direction.