The very first quilt I ever made, some 25 years ago, was a tied quilt that had the quilt backing pulled forward to make a binding. Being new at quilting, it just seemed logical to use that extra fabric. I still use that quilt and the binding doesn't show any more wear than the rest of the quilt. It's been washed and dried many times.
To me, it seems to be more economical to use this method, not
to mention easy and convenient. One of the books on quilting I got recently mentions this method, along with the other types. I don't see any issues with this type. As with other things in life, it often comes down to personal preference.