Regarding the scene in "Court Martial", note that the other officers were situated so that you never got a straight-on view of their insignia (I know, it was the same as Kirk's, but play along for a bit), whereas Kirk was right there, squared up with the camera, with that arrowhead insignia as plain as day. Likewise, in "The Tholian Web", in cases where an insignia would otherwise be visible, a strategically placed arm was covering it up, they were strapped down in the beds with the straps conveniently across the badges, or folks were just placed on their stomachs. In other instances, like Captain Tracy (and the other Exeter uniforms) or Commodore Decker, their insignia were shown quite clearly, and were most definitely not the standard arrowhead insignia.
I think it's clear that the intent was that every ship would have its own insignia, like every unit and ship in today's military has their own unit symbol, and when the budget was there, they followed up on that intent, while in cases where the budget wasn't there, they at least made an effort to obscure what otherwise would've been a distinctively non-Enterprise insignia.
I think it's clear that the intent was that every ship would have its own insignia, like every unit and ship in today's military has their own unit symbol, and when the budget was there, they followed up on that intent, while in cases where the budget wasn't there, they at least made an effort to obscure what otherwise would've been a distinctively non-Enterprise insignia.