I went on a training camp to malaysia and was coached by woong chong hann and as i understood following through was important for many reasons. The reason that most affects the game is that it makes it harder for your opponent to tell which shot you are doing since they all look the same and it's all about where in front of you the shuttle is being hit.
The second reason is stamina. When you follow through you use power from your whole body and not just the forearm. I often tell the people I'm coaching that if one use every part of your body a little, like putting speed on the upper body by swinging the non racket arm, using your abs to do the same or pushing with the back/shoulder combined with using the forearm is not as tiring as just using the forearm flick shot. It's almost impossible to have consistent shots for three sets when not following through. When following through you can play a lot more relaxed.
Also a lot about injuries and not having the jerks that comes with stopping the motion fast. But stopping the motion makes your arm slow your whole body down if everything but the arm continues forward. It gets you back into the court way faster if your whole body is going in one direction.
It also is the most natural way it's possible to play a clear, you don't see spear throwers (javelin) stopping their arm halfway through the throw. I think badminton players can learn a lot from their way of twisting the upper body to get power.
Hope it's helpful