My claim is backed up by Walter Matt Jefferies who stated that the Enterprise was meant to be the first bird, the first in the (its) series.
On a concept drawing. Originally the Enterprise was called SS Yorktown. The Defiant (NX-74205) was to be named USS Valiant. Things change.
No, not only the concept drawing. The quotes come additionally from the Star Trek Sketchbook
and interviews with Matt Jefferies (e.g. BBC Online)
Yes, things change but there is no indication whatsoever that "Enterprise Class" was not the proper sub-classification during the entire TOS production.
In a memo from 08-09-1967 (chief nitpicker) Bob Justman talks about "the names of the 12 ships of the Enterprise Starship Class". The first edition of The Making of Star Trek
was released in September 1968 and Stephen E. Whitfield had compiled this information from his interviews with the producers and the people involved: "The Enterprise
-class starships have ben in existence for about fourty years and are now capable of surveying and exploring the uncharted remainder of the galaxy."
Had the producers (Roddenberry and Justman) and the creator (Jefferies) settled for "Constitution Class" there would have never been any "Enterprise Class" reference in this book.
Maybe I should have merely asked one question "Why is the Enterprise not
a member of the Enterprise Class?"
Considering that J. & J. based their entire work on The Making of Star Trek
which contains these two references, I would have really liked to get an answer.
In the case of Greg Jein I assume it wasn't compatible with his pet theory, so he ignored it. Franz Joseph probably didn't care. As he said about himself, he wasn't a Star Trek fan.
Back to the original topic. I think it's safe to say that production-wise the Constellation's
registry was simply a re-arrangement of the AMT decals for the Enterprise
(did the original AMT model kit only contain "NCC-1701" to "play" with?).
Strictly in-universe, it's interesting to note that the last two digits coincidentally happen to be "17" as these usually come first for the Enterprise
(and other starships of the - cough - 17th design). The odds are 1:99.