Perhaps it is not the Enterprise that is 'special'. It has the same insignia as most Starships.
Perhaps the reason that Wesley's, Decker's and Tracey's ships have different insignia indicates that they are the special ships.
Wesley and Decker were Commodores and maybe their ships were more important than those commanded by lowly Captains.
As for Tracey's ship - I'm thinking maybe it was the flagship at the time. Not the Enterprise
My assumption in the Rise of the Federation
novels is that the Federation Starfleet was originally a looser merger of the founder worlds' space services, analogous to the European Space Agency today. Over time, the fleet became more integrated, but the distinct branches endured as administrative subdivisions of the fleet through at least the 2260s, since we did hear Kirk refer to the Enterprise
as a UESPA vessel on a couple of occasions. As shown in my uniform design sketch
, the various insignias we saw in TOS represent these various organizational divisions. The arrowhead, as we know from "Friendship One"
and the ENT enlisted rating patches
, is in fact the UESPA insignia from the 2060s onward. In my scheme, UESPA was in charge of the fleet's exploratory efforts. I used the Constellation
patch as the logo of the Andorian Guard (since it looks a bit like Andorian script), which was originally primarily responsible for military and defense operations; perhaps the Constellation
was assigned to patrol and defense duties rather than exploratory duties, and thus was under that branch of the administration. I used the Exeter
insignia for Alpha Centauri's space agency, which was a secondary research/exploration arm; originally it probably provided more just funding and resources than ships, but by the 23rd century it may endure as a distinct subfleet. And I used the Antares
insignia, which Justman's memo says was intended to represent the merchant marine, for the Tellarite space service, which I gave responsibility for operational support and supply. (Plus it looks kind of like a hoof.)
Or it could be that the fleet was reorganized at some point and the old insignias have been reassigned to the new subdivisions -- maybe they just represent the First Fleet, Second Fleet, Third Fleet, something like that.