Most plumbers in these parts don't carry 7/8 inch rods. Normally that is ok. However, when encountering a kitchen grease clog on a 4" line that can be an issue. With the smaller cutter only a small tunnel is bored into the grease. This can result in frequent clogging.
When a properly sized cutter is used the line is properly cleaned resulting in a far longer period inbetween cleanings.