This question is like asking how many street fights start by 2 people squaring up and having someone wave their hand between them and shouting "lets get it on". Punching and retracting the hand back to the hip is done during the basics and the patterns but not for sparring or in a real self defence situation.

There are many reasons for bringing the punching fist back to the hip. Some of the reasons I can think of:

1) Elbowing a rear opponent. For this one to work the 2nd opponent would have to be practically up against you.

2) Simplicity - one of the 1st things you learn when you begin Taekwondo is the horse riding stance mid section punch, when doing 2 punches like this (with the non-punching hand returning to the hip) both punches are exactly the same. When you do them in a forward stance or a back stance or from a guarding block one is more powerful than the other so it is easier to learn and to get the twist of the wrist right from the horse riding stance. Also if you are doing it for one technique simplicity demands you do it for all of them.

3) Hip involvement - goes back to point 2, most of the power in any single hand technique comes from twisting the hips so bringing the punching hand back to the hip puts it into the position for the next punch which starts at the point of rotation.

4) Retracting the striking hand - If your hand can retract your hand back to the hip as fast as you can finish your punch then you can retract your hand to avoid it getting grabbed as fast as you can punch. Going back to point 3 it also helps to improve your hip rotation with the push-pull action.

5) Speed - Because coming from the hip you have to move your hand further to get to the target than if you were punching from a guarding block. If you want to punch a target faster (get there in less time) you will have to punch faster from the hip so if you can punch fast from the hip how fast can you punch from the guarding position?

6) Grabbing something - Sometimes the retracting hand can be the result of grabbing your opponent and pulling them in to increase the power you hit them with, to make it harder for them to defend against it or to bring them closer to you. There are some movements in the Chang Hon patterns that do this, although not just to the hip such as the grab-chop in Won Hyo or the double elbow in Po Eun which could either be 2 elbows to 2 different opponents or grabbing with one hand, pulling them in and hitting them with the other.

I am sure there will be some that disagree and/or have other ideas but there you are.