Wow, it's always interesting when someone discovers something fans have been wondering about for over 40 years. That's not a dig, just an observation. I wish I still had Trek discoveries ahead of me.
Anyways, I also know they removed the insignia when haveing the unitofmrs cleaned, sweing them back on later. Some episodes (I think I saw it in a 3rd seasoner) you can see the tips separating from the shirt. Anyway, I think it was intentional because the opening overhead shot of the planet's surface used to be "flopped", as a reverse image. This was "corrected" for the DVDs, but it may have been intentional, since it happened a few times during the episode. Leaving off the insignia on Kirk's shirt would make that easier. Also, Sulu's badge was covered by the dog he was holding and everyone else had those coveralls.