I've always felt that the proper way to interpret stuff like this is, first off, put aside any and all fanon and other preconceived notions and to start with the only stuff we know for absolute certain, what's on screen, and examine it within the context in which it was created, not just the time in history, but the producers' intent at the time, and then build from there to come up with something that makes sense.
In this case, we know the producers' intent was that every ship had its own insignia, with the caveat that it's possible that Roddenberry didn't come up with that idea until the second season, or at least didn't have the budget to act on it until then. However, the fact that starbase personnel, for the most part, wore that starburst pin during the first season, and poor Commander Hanson on that Neutral Zone outpost with that fishlike pin, and the folks on the Antares, indicates that at least the germ of the idea was present from the very early stages.
Buuuuuuuuuuuut, we got that bar scene in "Court Martial", the girl in "The Menagerie", hell, even that sleasebag in "The Cage" (although that one can be explained as "Hey, Chirs, this is the guy who gets the Enterprise because you went into business on Orion"). An apparent contradiction.
The best reconciliation between the producers' intent, of every ship having its own insignia, and the scenes from before this intent was enacted, is that each fleet had its own insignia, with the starburst pin being the standard insignia for Starfleet. Around the time of TMP, the process began of making the arrowhead insignia the standard uniform insignia for all Starfleet personnel, starting with shipboard assignments, eventually getting to ground assignments (sometime after the loss of the Epsilon 9 station).