Cotton is favored because it's soft, durable and natural. Synthetic fibers sometimes don't feel as nice or hold up as well as cotton.
I can also tell if a cotton has been hand dyed or machine dyed just by the feel. A "blend" fabric will feel "squeaky" or even slightly slick or oily in your fingers.
Cotton is breathable, only shrinks once, holds dye marvelously, and lasts a LONG long time. Poly fabrics or blends do not take hot ironing (they will melt, shrink or distort). Also they do not hold creases well, making it difficult to iron seams in blocks and make them lay properly.
Rayon will not hold up to high heat in pressing. Silk will deteriorate over time. Many old "crazy" quilts with silks in them, the silk is crumbling away. Wool must be handled carefully, never temperature-shocked or agitated when washing, never dried in a hot dryer... otherwise it begins to "felt" and will continue to felt and shrink forever until it has reached its full point (as small and tight as the fabric will go).
These are reasons why cotton is preferred by quilters.
Quilter/quilting teacher with over 25 yrs. experience