It is my believe that the sine wave motion in ITF Taekwon-Do can be understood as the combination of Karate's linear way of moving with Taekkyeon's relaxed bouncing.
Look at the Karatekas in the video below. Notice their steps and how their bodies stay the same height.
Now look at this demonstration of Taekkyeon. Notice their relaxed "bouncing" by means of what we would call "knee spring" in Taekwon-Do.
Now imagine stepping like Karate, while combining it with the relaxed light-footedness found in Taekkyeon. What you get is something that looks very much like Karate, but at the same time resembles the relaxed "bounciness" of Taekkyeon.
The reason is simple: by means of the sine wave motion, ITF Taekwon-Do has incorporated the soft style wave principle from Taekkyeon into the Karate way of moving. ITF Taekwon-Do is merely the child of its two parents, hard style Karate and soft style Taekkyeon.