The binding gets the most wear. The best binding is cut on bias and folded in half, then sewn on. Next best is same but not on bias. Single is OK for very small quilts or wall hangings that do not get a lot of wear. It is OK to fold back to front but does not wear as well.
IMO corners that are not mitered are just not as attractive or finished looking. If I am going to spend a lot of time and money on a quilt, I want it too look it's best to the edge.
Kids or charity quilts I sew binding on back, turn to front and sew with decorative stitch. Others I always sew to front and blind stitch to back. Judges will look at binding for this as well as evenness of binding, same width front and back, binding full oif batting all the way to edge, and not wavy. Even if not making a quilt that will be judged, I try to practice this on all my quilts. The more I practice the better I get.