Personally, I believe you are looking at it a bit wrong... the most static components in the rigging setup are the pulley or ring at the anchor, and the lowering device. We'll ignore any redirects, for simplicity. Those two items are about as static as it gets. Neither one is going to give a little stretch in a misjudged negative rigging scenario. They're going to break, if nothing else in the system is weaker than they are, or if the dynamic elements aren't chosen carefully. If we assume the rope is chosen to be appropriate, and is weaker than those two items, then what is left is the fiber products attaching them to the tree. Having a dynamic element on both sides of the hardware reduces the impact loads that they see... if we used heavy chains or large dyneema products, the hardware will see a much greater amount of the forces. If the rope is more dynamic (i.e. nylon core) the forces are reduced, and the same goes for the attachment slings. If they are dynamic, then the hardware lies between two dynamic elements, and the impact forces are lower and spread out over more time.
The 12-strand hollow braid products work well because, although polyester doesn't match nylon for elongation, the rope construction allows more elongation. This is why 12-strand ropes like True Blue, etc. handle loads and shock forces that would seem a bit high for a 1/2" rope. One of the very best ropes for attachment slings, however, is Dynasorb/Polydyne or other nylon core rigging lines. They can show quite a bit of elongation, even in short lengths.
So, ideally, you would use a rigging line that is appropriate for the job, with dynamic attachment slings sized a little larger than the rigging line. The only benefit to using a static anchor, like dyneema, is in a static rigging scenario where control and low bounce/stretch are important. For dynamic rigging, a static anchor puts more impact forces on all of the rest of the system, and can break out anchor points, beat the bushings out of rigging blocks, bend fairleads on the friction brake, etc.
I have made attachment slings out of Amsteel and other extremely static materials. I wouldn't dream of using them in a dynamic rigging application. I have several big deadeye slings made from 5/8", 3/4" and even 7/8" Dynasorb/Polydyne and their ability to absorb shock forces, even in shorter lengths, is amazing.
