Prewashing fabric does more than control fugitive dyes and control shrinkage: It also removes a whole slew of fabric conditioners. Some conditioners interfere with the way fusible products bond; some are sizing that make thin or loosely woven fabric feel more substantial; some conditioners make a soft, short-staple cotton feel smoother and hide the fact that its threads are inherently weak and that the fabric will pill and wear out quickly. I have found, after washing a new fabric that seemed of reasonable quality, that it turned out to be very inferior. Sometimes I will choose not use this fabric in my quilts at all. Sometimes I will just choose not to use it for binding, where I want to use a stronger fabric.
In general, I find prewashing gives you a lot of useful information about the actual quality of the fabric you have bought, and helps you make choices about how to use it: in an heirloom quilt? in a baby blanket that will be washed frequently? In a wall hanging that is not likely to be washed at all after it is hung?