Let's talk lever arms.
The longer the lever, the more speed is generated at the same speed as a short lever - think Buddy Franklin winding up from 70m. For dog lovers think of the ball chucker thingy.
The longer the lever the more speed occurs at the end of the lever and the more velocity you can produce.
You'll see in any player who is kicking from beyond their comfortable raneg of further, alter their mechanics to incorporate a hook of some sort which is the body finding a way to provide extra force.
Another thing is that lefties make it look so easy as well as the ever so slight range of motion of rotation that they go through as they hook from the left to the middle, can allow for better sequencing and activation.
This is actually how the body is designed to move, you generate movement from the middle then the extremities come through like a whip.
The pelvis has a high muscle to tendon ration (fore produces) while the extremities have more tendon and elastic structures (force amplifiers) and in a correctly aligned body, a small amount of movement at the waist can produce large amounts of force elsewhere in the body, and this case the foot.
When you rotate at the waist, it generates a stretch reflex in the upper body which aids the turning of the leg. Think back to that ball chucker, you swing it back and the flimsy end rocks back like a thrower but as you change the direction from backwards to forwards, the bottom end of the chucker is moving forwards while the top end is still moving backwards. The stretch reflex is when the top end "catches up' to the bottom and starts to fling forward, faster then it normally could.
If you've got a strong middle that can handle these forces and provide the "fling back" mechanism of the ball chucker, then you'll have consistently good distance on your kicks.
The more relaxed sequencing of the kick will also mean you'll be less injury prone.
On the other hand though, more rotation isnlt better here as there will be more slack then power and it will be like swiping with a wet lettuce leaf versus Jon Snow's sword.
Only use as much rotation as you can handle and coordinate at a high level.
Looking at Buddy...
As he "lays back" and swings his leg back, he opens the kicking up which is from the rotation of his middle
As he swings his leg back through to make contact with the footy, you can see that his hip have squared back up as his leg acts as a whip with his foot still behind the lever and generating more velocity.
We've mostly talked about what the hips and lower extremities are doing but have look at his right shoulder too, as it starts backwards and rotates forwards, the opposite motion of the hip, creating even more velocity through torque.
I got the idea of this post from this article that goes into this concept in a bit more depth.
