In the beginning, "starship" was a very, very special term. Only 12 like her in the fleet!
Not quite: according to Kirk, for example the old tub
Archon had also been a starship.
The "only twelve" statement is never associated with the designation "starship", but only with the specific type of vessel that Kirk flies. It may well be that there were only 12-13 starships of that design in existence in "Tomorrow is Yesterday", but other designs of starship no doubt existed in considerable quantity - including the previous generation of starship designs, and the first examples of the next generation of starships.
Yeah, it seems that at some point after TOS, "starship" ceased to mean "big and bad interstellar vessel" and simply came to mean "interstellar vessel" - perhaps because all ships from that point on were at least as big and bad as the old starships had been.
Still, it would be nonsensical for Starfleet to designate one of its 2260s ship classes
Starship class when the word "starship" at that point already was a generic one for a certain category of vessels. It might be just slightly less nonsensical to say that Starfleet would write down the category of certain vessels on a brass plaque on the bridge, so that for example
Constitution,
Surya and
Fanboy class vessels would get their status as starship confirmed in writing. But the
Constitution,
Surya and
Fanboy designations would still have to exist in parallel with the "starship class" nomer, so that Starfleet could tell its various starship types apart.
Timo Saloniemi