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?