Cotton batting softens with every washing. That is one of its most endearing characteristics.
I am wondering if your expectations are more along the lines of modern puffy comforters than traditional quilts. Have you ever handled vintage quilts? They were all made with cotton batting, and all would be considered "thin" along the lines you describe. So it seems to me that the baby quilt you made is responding to use as I would have expected.
If you want a puffier quilt, then you may want to try a polyester batting such as Hobbs PolyDown. One advantage of poly over cotton batting is that the quilt will dry much faster (and will be puffier, similar to modern comforters).
Some people do double up Warm and Natural, or use a layer of W&N with a layer of polyester batting on top to add puff. The problem with two layers of W&N, especially in a large quilt, is that the quilt will become quite heavy. Some people like heavy quilts, but many do not. Aside from being heavy on top of you when you sleep, they can become quite difficult to handle because of the weight, especially when wet. Two layers of poly would be very puffy, but also very difficult to quilt.
I doubt that the fabric fading is due to organic fabrics. All cotton fabrics fade with exposure to light as well as to washing. In fact, fabrics are "fade rated" in terms of number of hours. I haven't checked in a long time, but I believe an industry standard of colorfastness is something like 70 hours of exposure to light these days.
The first quilt I ever made was a baby quilt using traditional cotton batting. I had the opportunity to see it about 20 years later. Knowing the mother, it had been washed and dried on hot many times. The binding was frayed and the fabrics were faded, but the quilt was still much loved and soft as a cloud to the touch. The owner used it on special occasions for newborn cousins.