When I first started trying to learn quilting, I remember reading that sheets did not make good backings because the tight weave was difficult to quilt thru.
However, back then, if it wasn't hand quilted, it wasn't a "real quilt", using those newfangled rotary cutters was considered "cheating", a pieced backing was frowned upon, and strip piecing wasn't a thing yet. (I remember how excited I was the first time I saw a quilt in a day book, lol.)
The first time I used a bedsheet as a backing, it was on a rail fence quilt I really wanted to finish to give to my son for his birthday, but I couldn't afford the fabric for the backing. I figured he was going to be mistreating it and dragging it around anyway, so I used an old sheet. He loved the backing! He said that it was so smooth on the back, that he didn't need a separate bed sheet, stopped using one altogether, and got much better at straightening up his bed, since all he had to do is smooth out his quilt!