The heavier the object you are swinging, the harder it is to change the motion. With a badminton racket, it is easier due to it's light weight. Tennis racket or baseball bat, much harder. I don't think there is much to gain after the impact. Most important is the motion from start, leading up to impact, and quality of the impact. I think afterwards, it's just a matter of preference, everyone has a different "technique" or "form". Of course, I'm just a recreational player.
I would say badminton is more about speed than power... because even trained girls with wimpy arms can smash harder than me...
You're not kidding, I can't count how many times I get taken to school by high school girls who train 5-6 days a week during their badminton season. I will take it one further. I believe it isn't so much speed or power, it's the consistent practice of playing and competing. When you combine the consistent repetitive act with speed and / or power, you have a dynamic result of pure awe. Take one away from the three, you get something less than pure awe.
in other sports the kinetic chain also uses deceleration to transfer energy. the elbow of a tennis server will slow down to transfer energy to the lower arm. energy is transfered by slowing down (also called the "whip effect- a whip handle is also stopped and then the whip cracks)
deceleration is an important part in energy transfer to the next link of the kinetic chain in all sports. probably that works better in badminton than in other sports because of the light racket. the arm can really be braced tightly so that all the energy goes into the wrist and racket.
doesn't work in other sports that well because the racket is heavier.
however probably energy transfer is not the only reason, more compact swings could be a benefit too.
The player that demonstrated in the first video you showed is regarded by many as the best player ever. No joke
In tennis, the follow through is a necessity due to the weight of the racket. At impact you need maximum racket head speed, but cannot safely "stop" the racket afterwards. In badminton, a "tapping" action is much more prevalent most of the time, rather than using a full follow through.
As a beginner I think it's important to focus on following through with the motion. It can otherwise create bad habits where your body gets stiff when you want the whip effect. If we are talking forehand overhead that is. It's a bit different on backhand.
Think the stop method is very good indeed. Nice loose arm then brake in impact. I often exaggerate this in warm ups to get my timing and compactness in my swing right
I was once a beginner who could hardly clear 3/4 now can clear diagonally easily and this method has been invaluable.