I recently have made two of the same inexpensive kits. One I followed the directions, the other I added 1 oz of oak after primary fermentation was complete.
Didn't tell the wife until she asked, but she thought the body of the second wine, with the oak added, was a little heavier or fuller. So I'd say addition of body as well as flavor and the added ability to age it longer are some benefits of adding oak.
Different goals can be met depending on when you add the oak. Plenty of info on this site about that.