I do it the same way you do and my bindings are always full. I think the fullness of your binding is determined by your "seam allowance" when you put the binding on your quilt. If you sew less that 1/4", your binding will not match up properly. I was taught this method at my LQS. I do LAQ for others and because there are so many ways to do the squaring up of a quilt, I never trim the quilts before I return them to their owners.
I also cut my binding to be 2-1/4" instead of 2-1/2" because my walking foot edge that I use as a guide is less than 1/4" from where the needle goes in and on my old machine I had no way to change my needle position. Now that I can control my needle position, I still use 2-1/4" cuts because I prefer a slightly narrower binding.