I've spent some time going through physics engine's sourcecode in Java like JBox2D, Phys2D (both 2D) and JBullet (3D).
I observed that, while the rigid bodies move and are mutated in each step, the collision shapes that are attached to them, are not. Instead, they always stay located around the coordinate origin. When checking two rigidbodies for collisions, a "translation" object is fetched from each and is used to translate the two checked shape's vertices (or other defining properties, depending on the shape type) to their attachment's world position on-the-fly. These information are then used to detect collisions and react to them.
I've concluded the main purpose is, that you can reuse the same shape instance for multiple bodies, as they are stateless in the described scenario and save some memory as the needed information are calculated on-the-fly in each step.
However, I currently see more advantage in mutating the shape's positional properties as in their member values. Each shape's aabb and vertices would change ONE TIME in each step, so you don't need to calculate the same vertices multiple times when intersecting one shape to multiple other ones. Plus, you could also change areal properties (damage deformation) of the shape, because it is only used by one body.
So the questions is:
Why is it common to use positionally immutable collision shapes instead of mutable ones?
Edit: Found quite the same question, but without much of an answer at Storing rigid body collision shapes in local or world coordinates