blssdwlf wrote:

If the TOS Enterprise is the "first bird" or the "first in (its) series" then she would be the lead ship of her own class or series. If so, why isn't the subclass (or class) named after the Enterprise then?
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How do we know it isn't? The
Making of Star Trek mentions twice "Enterprise Class", but maybe the producers felt something like that on the bridge dedication plaque
U.S.S. Enterprise
Enterprise Class
San Francisco, Calif.
looked odd and instead decided to go for "Starship Class". The idea of labeling other starships (that looked like the
Enterprise) with an NCC-16XX was entirely Greg Jein's conclusion (based on the "12 starships only" concept), adopted by Bjo Trimble's
Star Trek Concordance and the Okuda's
Encyclopedia, but not by Franz Joseph.
blssdwlf wrote:

Or if she's named after a theme, the "Starship" theme, then the theme spanned 10xx for the Constellation to 17xx for the Enterprise. It would be possible for the Enterprise to be the 1st ship of the 17th batch or series - although the question then is should not the first ship of that batch be NCC-1700?
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No. Especially if you read
how Greg Jein came to the conclusion the first ship of
his batch (16th...?

) should be "NCC-1700":
http://www.trekplace.com/article10.html
Instead of arriving at a theory based on facts, he made the "facts" fit his pet theory, i.e. "NCC-1700" is the (reverse) alphabetical beginning of "his" list and needed a ship name with a letter like A, B or C as in "Constitution".
In order to arrive there, he concluded from the Mark IX/01 designation of a ship's primary phaser of a starship of the Constitution Class that the "Mark IX/
01" was indicating
USS Enterprise!
But in the subsequent discussion (at the bottom) he suggested himself that a short ("complete") bar of the starship status display indicated a starship being constructed -
which exactly is the case with "NCC 17 00" in this starship status display! (Is the other number really "1664" or is it "1864", the NCC of
Reliant? 
).
Apparently, there was a ship like the
Enterprise in construction but hadn't yet received its two-digit number (which could also be a two-digit contact code that hadn't been assigned, yet).
I'm confident that what happened was rather simply that Franz Joseph copied and pasted the speculations of Greg Jein ("Mark IX/01" / "Constitution Class" / "NCC-1700") he liked.
Back in the 1970's tech-trekkers found themselves between a rock and a hard place: Was the
Star Trek Concordance correct (based on Greg Jein's speculations) or the
Starfleet Technical Manual (based on what FJ had adopted from Greg Jein)?
Apparently, everybody was relieved that J.J. at least agreed on the sub-class and the registry of NCC-1700 for the
Constitution, so this essentially "stuck" ever since and for decades I had believed myself this to be true, official and based on accurate research.
And then I became aware of what the actual creator of the
Enterprise had to say about the subject...
Given the erratic method how the original speculations had come into the world (twisted to match a pet theory), I couldn't help but to reconstitute the original and accurate intention for myself. YMMV
Bob