I do like the idea about the Starship Class indicating that the name above IS the class and not that the class is Starship. I do need to read TMOST -- there was another book I had called The World of Star Trek that I liked so I will check this out.
However, production wise, I imagine that wasn't a consideration. At the time, they were just beginning to build this universe and introduce it to the audience. One MAJOR detail that would need to be accurately conveyed to the 1960's audience is that this spaceship travels to worlds in other star systems
, not just to the moon or planets in our solar system. To help drive this point, a major emphasis was made on using the word STARSHIP instead of SPACESHIP or ROCKETSHIP (caps for emphasis, not for yelling). So I can this being the main driver at the time that plaque setpiece was made. This is a Starship. Different classes came later as the producers figured out the universe, and the audience became more familiar with it.