The question, whether a big rotation back of the shoulders matters, overlooks what really does matter. Also, in comparing the platform and pin-point servers, you're missing a key difference between those styles that matters, which is the orientation of their feet, which is always much more forward-pointing into launch than that of the big turn-back guys. I'll explain. You critique. It's about what coiling is, and what uncoiling does:
(This is long. Begin to read at your own risk. Nonetheless, I think it is essential material in differentiating and understanding the two main forms of serve.)
Forget all the blather about how in the uncoiling the point is to transfer energy (in foot pounds!) up, measured by Newtonian Ground Reaction Force. No! When you coil what you are doing is all about muscles, a sequence. Forget foot pounds of energy:
The main extensor (straightener) of the legs/knees is the Quadriceps Femoris on each leg, a group of four muscles that run from the tibia (calf bone) joined in one common tendon that runs through the patella, knee cap, until three of the four segments/fiber groups are anchored to the upper part of the upper leg, the femor. It is the fourth member of the Quads group that matters: It attaches to the Illium, the pelvic bone, on the same side as the Quad you are relaxing or contracting.
When you bend/flex the knees even a little, this relaxes the tug of the quads on the hips so that the hips can rotate back a bit in the "unit turn" in tension against the leg. You soon run out of room. The hips can't pull farther. The initial knee flex is mandatory for hip rotation.
You can test this for yourself: Stand with feet together, legs straight, and rotate your hips/torso clockwise, as in a forehand: You won't get far. Now repeat this test, but with your knees bent as in a serve (or forehand): Try to rotate back as in a forehand. You'll find that you can rotate your hips farther around because there is less tension from the quads on the hips. This is good. It means you'll get more power in your ultimate forward torso/shoulder rotation and therefore stably into your racquet head's velocity.
The torso rotators are the Abdominal Obliques, Interior and Exterior. They come in a pair on both sides, the interior and exterior oblique. The interior oblique on one side automatically works with the exterior oblique on your other side...to rotate the torso. The right exterior oblique when flexed rotates the torso to the left. The left interior oblique when flexed also rotates the torso to the left. The obliques are anchored at one end to the hips (illiac crest, pelvis) and at the other end to various ribs, since the muscle has many bands or threads at the rib-cage end. When the hips align with the femurs upon leg extension the obliques are triggered, tugged, and they pull the rib-cage medially, to the center.
In the unit-turn or turn-back preparing for a forehand or serve, then, you've bent your knees a little to allow the hips to turn farther back. On top of that you rotate your torso/shoulders even farther back than the hips, stretching one pair of the obliques: This "farther" turn-back of the shoulders (vis a vis the hips) is called attaining "separation angle." It is a key indicator that the forward stroke can be or will be fast. (ITF Handbook, "Coaching the Advanced Player: The Forehand.)
NOTE key to the great "turn back" question: For the coiling, the turning back, to be effective, you need to have at least on foot planted and facing slightly toward the net before final turn-back extent, relative to how far you rotate back. This is so that that leg’s femur is facing somewhat toward the net compared to the hips and torso, so that leg extension pulls the hips and torso in that direction. If you launch your forehand by extending the right leg, it is the right foot that must be planted BEFORE you have fully turned back. (You can, and many players do, plant the left foot more forward-pointing instead, but they must then shift their weight onto that left foot and extend the left leg to max torso rotation.) The planted foot provides a stop, ultimately, to the rotation of the hips back. That rotation needs to stop at some point so that the shoulders can turn back yet farther than the hips in tension. You'll figure out why when you read the uncoiling explanation below... (Laugh. If your hips are turned back farther than your shoulders/ribs, the whole uncoiling thing doesn’t work so well. Laugh.)
So, when in correct position rotated back in prep for a serve or forehand, you have flexed knees, a planted foot, hips turned back as much as is comfortable, and the torso/shoulders rotated back even farther (and you've taken your racquet back or up, of course). You’re ready to launch rotation: The quads were relaxed a bit by bending the knees, but then one thread was stretched a bit by hip rotation. The obliques are stretched by your rotation back of the chest/shoulders. You're ready to go: In the serve three things happen simultaneously: You throw the tossing arm forward, you extend your legs, you toss or throw the racquet back, down.
Extending the legs, i.e. straightening the knees, done by the Quads, simultaneously pulls on the pelvic connection of the quads, pulling the hips into alignment with the legs. (This alignment also happens when you perform the sequence in the opposite direction for a backhand. When the legs straighten, they pull the hips into alignment with the femurs no matter which way the hips were out of alignment the moment before...)
When the Quadraceps (quads) pulled the hips around to line up with the femurs (upper leg bones), the hips in turn pull on, trigger, the obliques, causing the torso to line up with the hips.
It is this muscle sequence that contain the meaning, the importance, of the "coiling and uncoiling," something almost all coaches leave as a mystery. I'm on very secure ground. "To err in teaching amounts to deliberate sin."
Once the legs have extended, they've done their job, fast or slow, and you might as well be in the air. Once the hips have lined up, they've done their job, rotating the torso. Once the torso, hips, and legs are lined up, the torso can still rotate farther, but the forearm, small shoulder muscles, the lats etc. add the last velocity and spin via internal shoulder rotation into contact, ISR.
SO, at last THE PAYOFF: You will notice, in your example photos, that the pin-point guys bring their back foot up and both feet, planted, are pointing more toward the net than the "big turn-back of the shoulders platform guys." The point? The Question is NOT how far you turn back, but how far your hips, then shoulders, are turned back relative to the planted foot. Both styles rely on triggering the uncoiling by extending the legs. The planted foot (or feet) just prior to launch determines the orientation of the femur, the final determinant of tension on the hips (Illium). There are other advantages to each style. I hope they're obvious. But, both styles are primarily subject to the effectiveness of the coil and the speed of extension, the uncoil.
There. I told you it was long, but you said you were Curious. Robert Ludlum writes at even greater length, but then his stories are more exciting...