(written from a Production point of view)
The D4-class was originally intended to serve as Vorok's battle cruiser in "Unexpected", the fifth episode of the new series, Star Trek: Enterprise. John Eaves and the rest of the team, understandably exhausted after the Enterprise pilot, were asked to do yet another design at the last minute. Eaves did, labeling it an "Klingon Battlecruiser "retro"", the D4-class designation later given to it at Foundation Imaging.   Eaves stated on his design process,
"I'm trying to retro the old Klingon battlecruiser. I took the old battlecruiser and took it back in time to the point where it's kind of held together by wires – kind of like the Golden Gate Bridge's technology. That long neck I thought at that time might be unstable so l got kind of a 3-piece pipe neck with heavy cables attached to the ship. Same with the engine – I didn't want framework because you see that so much so I went with cables: I thought this might be a neat thing and it has kind of a prehistory look to it, a real architecture that doesn't say framework. I just turned in the first pass on that and I'm waiting to see about it.
"In the script they kept calling for a retro warbird and we worked on that and it looked really good: it had a lot of motion on it. With the computer world now you can do all sorts of movement on a model which was discouraged before because to do motion control just required too much engineering to build into a model.
"You don't want to detail it like they did on The Motion Picture which was easy to do to bring it forward. It almost seems like that would have come before the smooth design – if you think about the whole series of the TV shows and movies you'd think that the really heavy detail look would be prior to the smooth look (of the '60s TV show ships). I tried to keep it smooth but segment the pieces so they're definite – this wing is a piece and this engine strut is a piece – as opposed to coming up with detail lines that went across the top. You see where this section is attached to that section and you see how these cables are designed to hold the piece together so it won't break off. So without going too heavy on the line work l changed the look of the engines and the way they work so it looks more industrial and there are more exposed pieces which you could easily cowl over later and you'd have the TV version." (Star Trek: Communicator issue 136)
Yet, the producers said that "its windows weren't prominent enough", a fact Eaves was very unhappy with.   The Star Trek: Communicator article stated that, due to time constraints, they ended up reusing the CGI battle cruiser model that was built for Star Trek: Deep Space Nine, and which had previously appeared in another discontinuity in the Star Trek: Voyager episode "Prophecy", as a D7 class battle cruiser.
A CGI model was built at Foundation, but it, as stated, was overruled. Taking a somewhat dimmer view, Rob Bonchune recalled the situation,
"The only other original design that was also chopped (that I remember now) was the John Eaves Klingon D-6 or D-5 [sic] that I included in my calendar image for 2006. It was originally done FOR FREE for Star Trek: Enterprise by Koji [Kuramura], who stayed up 36 hours to do it for the show. It looked great, but then the "producer(s)" said, "put more windows on it". We said "no" (you have to understand that we did so much extra, that at that point it was the straw that broke the camel's back when they were being mindlessly trivial and unappreciative). So, in their infinite wisdom, they choose to use a low-resolution K't'inga model (from a timeline over 100 years later) we had lying around. Because that was much more logical than a ship that needed 10 more windows that no one would EVER notice!!!!" Nevertheless, Kuramura himself expressed great pride in his build, "I had the great pleasure of building this model for Enterprise. But for reasons that were never clear, they decided to go with the older version of the Klingon ship that was based on the STMP Klingon ship. Which Jose [Perez] built. This was one of my favorite models that I got to build." wbm
As for the design itself, Bonchune has commented, "I guess my least favorite thing on it is the engines. They look like they are from Picard's time, not pre-O[riginal]S[eries]. However, the rest of it has that bulky primitive Klingony feel that I think would work. Always hard to reconcile today's FX abilities and expectations with trying to stay true to something looking more primitive than TOS."  , adding on another occasion, "Well, if we had aired the ship, I was going to refine the wings to be a little less "blunt trauma" to the aerodynamics. But when we got nixed, we moved on.....so, it stands as is."  Apart from the August spread in the 2006 calendar, the model also found its way on the back cover of the Ships of the Line book. wbm
Years later, in 2008, Eaves resubmitted his design as a possible contender for use as the Klingon warbird in the re-imagined Star Trek (2009). While the design as is, was not used in the movie, its lines were followed by Visual Effects Art Director Alex Jaeger. (Star Trek - The Art of the Film, pp. 56-57) The class designation however, was brought back for the alternate reality D4 class in the 2013 feature, Star Trek Into Darkness.