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