The biggest advantage I've found to using the insert is that by the time I'm done brewing coffee (using a sheet of titanium foil and a couple of paper clips to make a holder for the filter, putting the stove together, breaking twigs…) the other Boy Scout leaders know that I'm serious about this cup of coffee and they'd better leave me the heck alone till it's finished.
More seriously, I use the insert and the heat shield when I'm in wood-burning mode as a way to help instill just a tiny bit more Leave No Trace thinking when I'm around the boys. Haven't done any comparative testing but it doesn't seem to really make the wood burn a lot better than it would in just a pile on the ground.