Star Trek: The Next Generation first aired in 1987 and is set in 2364. Now, the Enterprise-A was first unveiled in 1986 at the end of The Voyage Home 2286. My question is this: why did the producers decide to name the Enterprise in TNG the Enterprise-D? Why not the Enterprise-C? (I can understand not referring to it as the 'B' because it was reasonable to expect there would be another ship named Enterprise between the decommissioning of the 'A' and 2364). I'm looking for behind-the-scenes information provided by the producers or other staff involved in the production of the series if it is available.
Actually, it was originally intended to be the Enterprise-7, until The Voyage Home introduced an alphabetic designation for further Enterprises. Even after that, it was initially designated the Enterprise-G (!) by producers.
From Memory Alpha:
During the early planning stages of TNG, it was intended for the series to be set in the late 25th century. The Enterprise-D would have been the seventh starship to bear the name, with a registry of NCC-1701-7. After the release of Star Trek IV: The Voyage Home featuring the USS Enterprise-A, the designation was changed to NCC-1701-G before the producers finally moved the series to eighty years after The Original Series and settled on NCC-1701-D.
Basically, the producers felt that there should be about seven Enterprises in a 150-year period — a service life of just over 20 years.
Incidentally, the article also says:
There was also talk of eliminating the starship from the TNG series altogether and merely boosting the abilities of the transporter, but this idea was quickly dropped.
So, if some producers had their way, there would have been no Enterprise-D at all!
Because of age (decommission) and destruction.
Registry: USS Enterprise (NCC-1701)
Service: 2245–2285 (40 Years)
Destroyed in the movie Star Trek III
Registry: USS Enterprise (NCC-1701-A)
Class: Constitution refit
Service: 2286–2293 (7 Years)
Captain: James T. Kirk (William Shatner)
Decommissioned due to newer technology in Star Trek IV
In a non-canon novel it was destroyed "The Ashes of Eden (1996)"
Registry: USS Enterprise (NCC-1701-B)
Class: Excelsior refit
Service: 2293–2329 (37 Years)
After that much time it was decommissioned due to age.
Registry: USS Enterprise (NCC-1701-C)
Service: 2332 – 2344 (12 Years)
It was destroyed attempting to defend the Klingon outpost Narendra III from Romulan attack. "Yesterday's Enterprise" (1990)
Registry: USS Enterprise (NCC-1701-D)
Service: 2363–2371 (8 Years)
Destroyed by Romulan Attack during the move "Star Trek Generations"
This information came from https://en.wikipedia.org/wiki/Starship_Enterprise but you can find it many places.
The simple answer is time and the destruction of ships. Some of them were destroyed in the movies and some of them were just too old or newer technology came out and had to be decommissioned. It's just a simple matter of the timeline when TNG started.
My Guess, this was good public relations. It was a special honor given to Kirk's Enterprise after saving Earth. Since they had been such a visible symbol of Starfleet, it was a nice way to honor them. One outlook was that original metal from the Enterprise was scrapped and recycled to build the new one. This is not uncommon in real ships. Steel from the USS Enterprise (CVN-65) has been used in the construction of it's successor (CVN-80).
The Enterprise-A was obvious, Starfleet was looking for a special "punishment" so they pushed through a contract for the renaming and recommissioning of an older Constitution class hull and with Kirk in mind they made that contract number 1701-A. It could also be a form of Naval tradition in a sense of real ships, the USS Constitution is the "Oldest ship still commissioned. I suspect this is out of nostalgia.