One possible explanation is that the Exeter wasn't a Constitution class, there were outward similarities and design concepts, but it was of a class preceding the Constitutions.
The same story with the Constellation in Doomsday Machine, different class from both the Enterprise and Exeter. Between them three classes of starships.
Kirk in Tomorrow is Yesterday said there was only a (bakers?) dozen like the Enterprise in the fleet, Starfleet might change it's ship building requirements frequently to deal with new knowledge and changing conditions.
And so a new class is born
Well that does seem to be how the Klingon Empire does it.