And to recap, if the Enterprise was either "Starship Class" or "Constitution Class" she cannot be the "1st bird of the 17th design" as she is not the lead ship.
Not necessarily. After all, the HMS_Afridi
was the lead ship of the Tribal-Class
yet neither she nor any of her sister ships were called the "HMS Tribal".
Timo referred to the British River
Classes earlier where the class of ships are defined by a theme
and not the lead ship's name so I get your point.
If "Starship Class" was a theme that was replaced temporarily by "Enterprise Class" from TWOK and then again replaced as "Constitution Class" in TUC it would suggest a shift from naming by theme to naming by actual lead ship.
With Picard calling the TOS bridge "Constitution Class" and Scotty acknowledging him, then we can assume then in the TNG version that "Starship Class" was either a theme that encompassed the "Constitution" sub-Class or vice-versa, IMHO.