If you look at the ripped edges under a microscope, you will see that there is damage to the fibers extending about a half-inch in from the rip. This damage won't show up immediately, but over time seams along those edges will be more likely to pull apart and fray. This means a utility quilt might not last as long as it otherwise would, and is of particular concern to quilters interested in making heirloom quilts that are to be passed down through the generations.
I would have no problem ripping fabric along the length of grain for a border, but I would rip it at least one or two inches wider so I could cut off any damage from each side.