My maternal grandmother used sheets all the time. I have a quilt that she gave me 40 years ago and the back is holding up a lot better than the pieced top.
Of course, back then, the sheets were all cotton.
I just recently used my Joann's coupon to buy cute fleece to back two baby quilts. I like using alternative materials for backing. I have found that the backings take more abuse that the tops especially the lap/snuggle quilts since there's no sheets between them and the people using them.