People have been using sheets for backs for years. However, there is a reason it isn't recommended. One is the problem with cotton and synthetic blends, but the real issue is that most sheets we want on our beds are soft, which usually means a high thread count. This high thread count makes needling through it a bear. This would be more noticeable with hand quilting.
I did make a quilt many years ago, using an old super percale sheet on the front and the back. I used a thermal blanket as the batting, and tied the quilt. Out of all my quilts that was the most heavenly one to use! My kids would fight over it, on son took it away with him, and it got snatched by another son. The quilt has been retired though, it was just way too raggedy!