I never understood the fuss regarding class.
I'd dare to say it didn't exist in the beginning. The Making of Star Trek
states on the first pages that the original draft had the Enterprise
to be a member of the "Cruiser Class" (another hint that the debated Matt Jefferies' preproduction sketch is a genuine work from the 1960's) before they changed it to "Starship Class".
Roddenberry wanted to have a series palatable to international audiences and not just pigeonholed for US audiences (hence United Space Ship, hence "NCC" as a mixture of US and Soviet naval prefixes, hence alphabetic Starship sub-classifications reminiscient of the Soviet Navy and not the US Navy).
"Starship" can be translated into all languages (including the alien ones of the UFP) and therefore had no preference for a certain nation.
But apparently US script writers for Star Trek (like Gene Coon?) didn't subscribe to Gene's philosophy and suddenly we had the "Constitution Class" in the "Space Seed" script and the primary phaser schematic.
Especially considering the debate we are still having, it's not too farfetched to assume that people like Matt Jefferies and Bob Justman didn't like that idea. If
to be, yet, another classification then it would be "Enterprise Class" for NCC-1701 and therefore "Enterprise Class" is twice mentioned in The Making of Star Trek
to exactly avoid the kind of confusion that came from this "Constitution Class" reference.
In the interviews Matt Jefferies gave in the early 2000's there is no reference to either "Constitution Class" or "Enterprise Class".
That's not surprising, if he had been from the start an advocate of "Starship Class" and nothing else.
Apparently he revisited his original preproduction sketch of the TOS Enterprise
and merely restated how it was supposed to be, i.e. that the Enterprise was the "first bird", the "first of the [17th design] series."
To avoid stepping on anybody's toes, courteous as he was, he left it to us to draw or ignore the conclusions from his statements, IMHO.
I'm sorry, but I find myself unable to interprete the "first bird" as anything else than the first ship of its kind.
Franz Joseph might have been an expert of the Jupiter II
, Greg Jein is most definitely the expert of ADC 2238-5531, but when it comes to NCC-1701 I consider its creator the ultimate authority.