I don't see the logic in having one of the letter include the name of the ship's class in the registry...
Just a way of breaking down each series of ship types further, each series of ship types is divided into 26 sub-series or classes. Each class is name for the next letter in the alphabetic sequence. The C-series would be classes 53 (A) through 78 (Z).
If the Federation had been around for a thousand years, maybe. A little over a century, I don't think so.
At thousand years? Maybe not. When the Federation was first formed, the various original members had their own fleets. I think that after the Fedration was formed the members kept much of their fleets, however the units that were transferred into Federation service would have been consolidated into Starfleet. These ships would have been given new identification under Starfleet's identification system (largely would have kept their original names). These alone would account for dozens of ship classes.
Many subsequent new members would also transfer some of their ships into Starfleet, which would also need to be re-identified as well. In addition, there would be ships purposefully built solely for Starfleet's use throughout the first century, not just cruisers and destroyers, but multiple surveyors, tugs, tenders, transports. After a single century there could easily be 55 classes. Probably more than 55 classes.
The Constitution's are a somewhat older ship, if the Enterprise is the 17th design within her class, that makes her the 16 variant. Each variant might only have a few ships each.
Kirk, in reference to the Enterprise, said; "
There are only 12 like her in the fleet."
By Kirk's era, Starfleet might be composed of several hundred ships (maybe thousands), of a wide variety of classes.
This all is just shear conjecture on my part.
