Why did some vessels in the 23rd Century use unique assignment patches?

Question

There may be no in-universe answer to this question, but I'm curious about anything people can find.

In Star Trek: The Original Series, a distinct assignment patch was used for each vessel or starbase. Starfleet Command used an elaborate star, while the Antares, Constellation, Exeter, and Defiant were seen to use some rather unusual geometric shapes - and, of course, the Enterprise used the familiar delta insignia. These seem like the spiritual successor to the NASA-style patches used in Enterprise (the series).

In the reboot films, we saw the arrowhead insignia used by the Kelvin and, in the 22nd Century, by the Franklin. Since this is an attractive and seemingly significant symbol (since it eventually becomes the icon of all of Starfleet), it seems natural that it might have been reused.

But this theory is torpedoed in Discovery, where we see the same insignia being worn by the crew of the Shenzhou and Discovery, as well as Starfleet Command (and, I believe, crew from other ships). Clearly, the symbol's use as the insignia of all of Starfleet predates the usage of individual assignment patches.

My question is then, therefore, has there ever been canon or word-of-god/behind-the-scenes justification for the use of distinct assignment patches in the 23rd Century?

Answer 1

According to Bob Justman the different patches were a production error but explained as not proper Starfleet personnel.

But according to a memo from Bob Justman, "Star Trek" associate producer, to William Ware Theiss, series costume designer, Gene Roddenberry had confirmed that “all starship personnel wear the starship emblem that we have established for our Enterprise crew members to wear.”

Dated Dec. 18, 1967, the memo is part of the “Gene Roddenberry Star Trek Television Series Collection, 1966-1969,” stored in the Film, Television, and Theater Archival Collections at the University of California at Los Angeles.

“Doubtless this situation has arisen due to the fact that a different starship emblem was used last season on 'Charlie X,'" Justman wrote. “However, the personnel of that other ship in that show were the equivalent of merchant marine or freighter personnel — and therefore not entitled to bear this proud insignia on their individual and collective breasts.

“Please do not do anything to correct this understandable mistake in the present episode ("The Omega Glory”). However, should we have Starfleet personnel in any other episodes, please make certain that they wear the proper emblem.”

It’s interesting to note that the Enterprise’s insignia was actually intended to be Starfleet's from the beginning and that the scenes showing the Exeter and Constellation patches were production mistakes.

Later, in the third season episode “The Tholian Web,” Justman’s notes were followed for the dead crew of the USS Defiant; however, the appearance of the Enterprise/Starfleet insignia on uniforms was discreetly used, perhaps to avoid the inevitable confusion that it would cause with astute viewers.

^Source