I just went to the Sword and Brush figure show in Toronto this past weekend. While judging is a little different in that they use the open system, they still do have "best of" categories which are directly competitive. Regardless, all the names were plainly visible and everyone knew what everyone else entered and the sky didn't fall.
I suspect this tradition does more for the perception of objectivity rather than objectivity itself. As Dak points out, a lot of the time, especially at local shows, judges have a good idea who entered what anyways, and are pretty objective regardless. I don't think it does much for actual objectivity; it's just a little piece of theatre to make the entrants feel better.
Finally... Dak makes a good point in that there are benefits to having names public. In the world of social media, if someone made a piece you like, you can look that person up and talk to them about it, maybe make a new friend (which is way more valuable than a plaque or a deal in the vendor hall), or ask them for advice. I once had someone try to look me up after a show because he liked one of my pieces, but since my name wasn't visible, there was a lot of "hey, does anyone know who made this?"