In reply to Stefan Jacobsen:
> I'm not sure what you mean. In the Loop haul case, they don't use the other end of the rope, rather a unused loop of the same rope is sent down to the victim. Both climbers are still tied in to each end.
Sorry, should have said another part, not end, of the rope.
If you look at the other two example on that web page the scenario is probably following what looks like a natural one of:
1. get dragged over onto your butt/face. Build anchor.
2. clip trax to anchor to escape system and catch one's breath.
3. figure out what to do next by visiting the edge
4. set up system and haul, with the trax still in place and not having been moved.
With the loop method - as shown - there is either the need to remove the trax and replace it further up the line (this is easy if you have done lots of stuff with prusiks before, but isn't obvious to a beginner), or start by tying the guy off with a clove hitch and hence know right from the start you will be doing a loop haul - before you have visited the edge.
The only logic I can see for not setting this up how one would in a rock climbing situation is that it means it will be easier to pad both moving lines, therefore less friction, and that the guy will find it easier to do the final exit as the ropes will be less cut into the side.