But the ancient Archon
was also a starship...
I think that there's a major hurdle in terms of, well, mental aesthetics for any attempt to pin a "Starship class" identity exclusively on ships identical to Kirk's. Sure, there may be hundreds of classes of starship of which only one is named Starship class, but it's somewhat unlikely and unsatisfactory. Except of course if there once was a ship named Starship
that gave rise to an entire category of spacecraft, much like there once was a ship named Dreadnought
that transformed naval terminology. But clearly that ship would not have been the first of the design that Kirk currently flies, but rather a far more ancient vessel.
Much more fruitful IMHO to insist, even in the exclusive TOS context, that "Starship class" is a supercategory that covers a great number of designs from a long period of history, just like in the dialogue of TOS (c.f. the Archon
). Beyond that, it's a free-for-all: perhaps Kirk's specific ship was of Bonhomme Richard
class during TOS, Enterprise
class during TMP, then Constitution
class again during ST2/3, the ship staying the same but the class leader changing with each refit as different ships would have spearheaded different refits. Back in TOS, such fleeting things would not have been mentioned in the dedication plaque... But later on, new plaques would be bolted on at the conclusion of major refits, specifying the nature of that refit by spelling out the new class name.