Making and doing the binding is one of my favourite aspects of quiltmaking (probably weird, but there you go!). I do believe a separate binding would be more durable, and it makes a nice frame for the quilt.

the edge of the quilt takes more friction there for more wear so a double layer going over that edge makes sense--no matter how you put it on---unless the police have a say then its there rules that matter

It is a personal preference and no right or wrong way. I just like to put a binding on because I feel it makes a nice frame for the quilt.

My MIL taught me to bind quilts using the backing fabric and some of the quilts at the farm are over 100 years old and were made by her grandmother. The binding on them are very worn but so is the rest of the quilt. If it is a special quilt, I make a separate binding. If it is a use it every day quilt, I often self bind it using the backing fabric. These types of quilts will not be heirlooms and will literally be worn and washed to shreds. I figure the self binding will last as long as the rest of the quilt.

I've also used the facing way. I like the way it looks, I get a much needed clean edge. I make a folded strip, sew to the edge, flip and hand stitch or machine stitch .