I always press the binding in half before attaching to the quilt. It lays flatter for me. Also if there are bobbles cut in the binding they can be straightened up in the sewing process or trimmed if necessary. it is also easier in doing corners and joining the binding.
After the binding is attached by the machine, I then irong it from the front. This creases the sewing line and makes it lay flatter.I press from the top and into the corners which also make it easier to do the mitre.
Everyone has their opinion but this works better for me.