They didn't even try to add any futuristic or fancy-looking things
Maybe the production designer and/or JJ/production team actually liked the look? That doesn't mean you have to like it, but it may not have been an oversight.
I don't believe that TeutonicNights meant to imply an oversight, just bizarre thinking on the part of Abrams and his production team.
In STVI, when the Enterprise officers are being briefed that they're going to escort Gorkon to the peace conference, the room that they are in consists of a table, a podium, and nothing else. Like a theater stage, everything out of view is simply black. The reason is that they filmed it in an open space in a church, and didn't put up any more set than the table and podium.
Did people complain about that? (maybe they did, I wasn't participating in Trek conversations in those days). I mean, that wasn't even a "bad" design, that was really an example of no design. It may have partially been a budget issue, but ultimately it was an artistic decision, that the set would be undefined other than the props necessary for the scene. Did people argue that this was lazy or bad film making, that the room didn't look like an "official" meeting room, that nobody in "real life" would use such stark mood lighting in a daytime meeting that the entire room would be completely blacked out other than the meeting table?
Although that is an example of cheap and/or frugal production design, and is hardly the most inspiring set dressing in the world, it's never struck me as especially incongruous. The sparsity of the location works in the scene's favour, and connotes something of the stuffy, rote-like way the decimation of the Klingon Empire is discussed, and the manner in which Kirk is matter-of-factly told he's to be the Federation's "first olive branch". In short, it brings forward ideas and establishes a certain mood, making it good for the scene and good for the film. Also, the meeting feels somewhat hastily-assembled and secretive, which the small, unassuming room gives a measure of credence to. Finally, a note about that table: in its sleek, polished blackness, the table suggests something about Starfleet's refined nature, as well as dominating the centre of the room and lending the scene an ominous, funereal air (greatly supported by the film's Shakespearean title and Cliff Eidelman's dark main theme).
For all my issues with Nicholas Meyer, he had some good people around him for TUC and steered the ship well, and he even taught this then-eight-year-old some interesting words and phrases (including the aforementioned "olive branch"), as well as concepts pertaining to history and racism, which I remain grateful for, so maybe this is just sentiment talking. On the other hand, I do think the scene you've drawn attention to is far more artfully done, being a sobering thing in service of the film's plot and hemmed themes, rather than the overblown engineering scenes in STXI, which primarily, to my way of thinking, exist to accentuate the film's very antithetical (not to mention anachronistic) "steam punk" look, and to provide chintzy, soda-pop thrills, which might put bums on seats but tend to degrade the artistic property they've been welded to.
Honestly, what you've come out with isn't even a good example. The STVI briefing scene can't really be compared with STXI's engineering scenes. A much better comparison is with STXI's scenes at Starfleet Academy; specifically, the scenes in the auditorium featuring Kirk. Now, not only are you talking about a similar fictional place belonging to the same fictional organisation, but a place with barely any set dressing that has a similar function in real life (i.e. as a formal place of meeting/discussion). I'm talking about
Long Beach City Hall, located at 333 W. Ocean Blvd, CA. This was digitally extended by a VFX house, but done so thinly that it's blatantly the same interior, and even contains a noticeable visual artifact, where, if I had guess, the real-life central podium wasn't painted out correctly (the artifact I'm talking about is a faint blue square just in front of the stair rail, which persists as the camera pans up to Spock, exactly where the podium should be, for the duration that the relevant area of floor is visible). Here:
http://s5.photobucket.com/albums/y178/0Cryogenic0/?action=view¤t=lbc_vs_stxi.jpg
Is it "realistic" to have brewing tanks on the Enterprise? Well, if it were Battlestar Galactica, where everyone has their own private distillery, maybe.

But for the USS Enterprise, of course it's not. And the questions if it was budgetary or an oversight is moot—it made it into the final movie, so at that point it becomes an artistic choice.
Very little in Star Trek is inherently "realistic", by accident or design. But there is something in Star Trek,
especially in regards to the Enterprise, that aspires to verisimilitude -- that is, the quality of
seeming to be real or true. While no-one can say for certain that a mass of water pipes is inherently less realistic than power conduits and bulkheads, it is an affront to ST's clean futurism to include something so visually discombobulated, OTT and so recognisably "20th Century"-like, especially in the heart of the series' flagship vessel, which has always existed as a synthesis of optimism and rationalism, and as a symbol of high technology partnered with high mindedness. The appearance of fluorescent lights, painted walls and beams, pipes with nuts and bolts, and characters being accidentally beamed inside a network of pipes, with a tedious and simplistic Saturday matinee-esque action dilemma, seriously goes against the flow (pardon the pun) of what ST is and should be about.
And for me I focused on only the actors and actions; as long as the props (tables, chairs) were accurate enough to not pull me out of the space, that's what matters to me ... A movie is not a theater play, and the same rules do not apply. But ultimately, the point is the action and the actors, and if someone is drawn in by the events and the performances, the set becomes peripheral.
You said it yourself (
as bolded): films and plays are different. Production design is a critical component of motion picture making, and if someone in the movie industry thinks it isn't, then they're in the wrong business. Theatre plays give primacy to the written word and the way it's manipulated into drama; films give primacy to the frame and the way it's assembled for visual narrative. There is a
world of difference between the two. Unfortunately, few film-goers credibly understand this, and even some filmmakers don't really get it. Production design can, and does, make all the difference.
Could "Lawrence Of Arabia" have been filmed in a grocery store? Should the astronauts in "Apollo 13" have been wearing togas and leotards? Would it have been OK if Peter Jackson just used a piece of Blu-Tack for the One Ring in "The Lord Of The Rings"? For sure, these are extreme examples, but extreme examples prove the rule. The best filmmakers take production design very seriously, going to great lengths to get it right, from costumes and sets, to props and lighting. I couldn't imagine watching David Fincher's "Fight Club" without all that grubbiness, etched into the walls, the floors, the doors, the ceilings, the tables, the chairs, the actors' faces, why, the film grain itself, or "Lost In Translation" without the urban wonder of Tokyo, embodied in its clean streets, its twinkling signs, its modern architecture, its density, its complexity, its strangeness and its beauty.