I took a class quite a few years ago from Roxanne McElroy. (Her daughter, Deirdre, runs the company now.) Roxanne said that silk batting was her very favorite -- easy to hand quilt, and the result was very soft. She passed around a quilt with silk batting and it was wonderful. I believe silk is supposed to keep you warm in winter and cool in summer, but I'm not sure about that.
The biggest reason silk batting has not become more popular over the years is probably because of its cost. I don't know about now, but 100% silk batting used to cost about 10 times what 100% cotton batting cost.
Silk batting is especially desirable for quilted garments because it keeps the fabric thin and soft, not stiff.