As a Navy brat, I speculated that Theiss was going for something similar to the USN warfare badges, where the badges represent what part of the service you were in and/or your qualifications.
It's an interesting idea, and I've thought about it before. I think it has some things going against it, though. First of all, in the mid-'60s there were wings for aviation and dolphins for submariners, and that was it. The SWO water wings didn't come around till 1975, so when TOS was being made your typical blackshoe cruiser or destroyer officer didn't have any bling above the ribbons, much less your typical sailor. So I'm not sure how much that would have occurred to Theiss.
The other thing is, once you qualify, you wear that pin, regardless of assignment. The crew of destroyer A will have the same basic assortment of pins as destroyer B, because the qualifications needed to run destroyers will be similar across the board. I have a hard time imagining a reason why Kirk and his whole crew would have one set of qualifications, and Tracey and his crew a whole different set.