The state of NBC must be really bad if they can't even get people to watch one of the best shows on TV. The fact that they're shopping it around leads me to believe that they already know that the shows quality is too good for them.
I can't agree at all that it reflects negatively on the state of NBC to market the show. At its core, the show is fundamentally unmarketable to the mass audience, it's a show which is impenetrable if it has not been viewed from the beginning, and it is layered in off-putting elements that serve as a barrier to individuals even beginning to watch the show, let alone sticking with it.
First, it encounters the issue of it being seen as a cheap cash-in upon the title character. Where once an association with Hannibal Lecter would have been seen as something easily marketable, particularly in the wake of "Silence of the Lambs", after "Red Dragon", and more so "Hannibal" and "Hannibal Rising", this association may seen to be toxic. The character began to lose its allure as it became campier, lost the endearing qualities it once possessed, and gradually turned into a poorly written parody of what it once was, all the while finding it in material of a progressively lower quality. While shows based on existing properties have found success recently (Fargo, and the Marvel comic book shows really), at the time of the first season's airing who could be blamed for being apprehensive that this was yet another cash-in on an existing property which had become increasingly campy and milked? This declining quality was not, remotely, assisted by the increasingly macabre visuals which served little purpose other than to push shock value into new realms and dilute the once thrilling story into an exercise in presenting the viewers with substance-less images of great cruelty, substituting genuinely strong story-telling for shallow shocks. Second, it faced another problem; the lack of Anthony Hopkins playing Hannibal Lecter. To so many, Hopkins' performance was an absolutely character-defining performance in "Silence of the Lambs" and was seen, definitively, as Hannibal Lecter. Having seen his performance, it is nearly impossible to envisage any other in the role as he injected him with an incredibly sinister and endearing performance which elevated the writing. Not having Anthony Hopkins not only enhances the perception that it's a cheap cash-in ("they couldn't even get
the Hannibal Lecter to play the character?"), but serves as a barrier as people may perceive it to be unwatchable as there existing image of Hannibal Lecter is tied too closely to Hopkins' performance to be able to watch a Hopkins-less Lecter. Third, the concept of the show, revolving around great cruelty and a distressing concept is an immediate barrier of entry. Unlike CSI, Dexter, or Criminal Minds, there is no promise of seeing the great evil be brought to justice, nor is there any readily apparent ambiguity nor redemptive arc to be seen here. The distressing imagery that's marketed, while beautiful and definitely one of the show's strongest aspects, not only plays back into the narrative of the "Hannibal" license being increasingly diluted and reliant on little but shockingly graphic images, but does not make this a show which can be watched by much of the family. Hannibal has little readily apparent redeeming qualities, and the show does little to suggest a light at the end of the tunnel. That, too, is not helped by fact that Hannibal is a cannibal, which when combined with the lack of redeeming qualities, works against the show.
These turn out not to necessarily be particularly valid, but all of those serve as potential barriers of entry to somebody who has only heard of Hannibal in passing, or seen a small portion of the marketing, but even for somebody who knows a little more, and tries to get into the show, there are issues.
Fourth, the pacing of the show is without a doubt the largest barrier. For viewers who give the show a chance, it moves at a very, very deliberate pace. Viewers who are accustomed to something like Breaking Bad (which is kind of funny, as that, itself, was quite deliberate in pacing but had a tendency to ramp up at a roaring speed), CSI, Dexter, or a host of more popular shows, may be completely taken aback by the pacing of the show. The show moves at a deceptive pace, where much of the progress is portrayed through the development of a character, the progression of the imagery, or an internal shift rather than external and physical actions. Actions also take a considerable length of time for there to be any pay-off and may make the perceptive of the show's pace deceptive (Season 1 being seen as a procedural is the most blatant; despite many having seen the entire season they still see it as procedural despite it all building up and linking later). There are very few action sequences in the entire show, it is generally a psychological horror which is thrilling due to the character interactions rather than physical happenings. Fifth, which also ties in very much to the pace, is that the show is heavily told through visuals, and these become increasingly more abstract, symbolic, important (to the understanding of the characters, their motive, and the plot itself), and prominent as the show progresses further from the beginning. This style of narrative does not appeal to everyone, and can give off an air of pretentiousness (I would argue strongly that it's not pretentious as the style of narrative is absolutely back by a quality show full of substance, but not everybody may feel that way and some definitely believe it is just shallow and self-indulgent). As the narrative style is also very surreal, nightmarish, and strikingly alien from pretty much any other show that currently airs, it may be too great of a departure for people to stick with. Sixth, the writing of the show, in fitting with the narrative style where the show occupies a nightmarish version of reality full of abstract and symbolic imagery, is also filled with imagery and is not particularly direct. Motive and meaning must be intuited and requires engagement with the viewer. It's not natural, it's generally vague and otherworldly. How certain phrases appear relevant, how characters act and react, and the meaning behind what was said is not always clear, and a lot of times the concepts which are discussed are not entirely common knowledge (Will's Many-Worlds rationalisation in the second episode of season three, and the relevance it has to the ending of the episode a blatant example). This also enhances the feeling that things are going at a snail's pace, and as the writing becomes increasingly loftier the show is constantly challenging the viewers' expectations and tolerance to the style of the show. Seventh, the atmosphere, itself, is off-putting. The show constantly emanates dread, horror, and discomfort. The imagery is consistently nightmarish, the characters constantly face displays of great cruelty, the characters all becoming increasingly tortured, people encounter operatic levels of violence, and the viewer becomes more entrenched in blood as the show progresses. It is no surprise that, for some, even having started the show and watched for awhile, that they simply cannot watch in horror any more. Finally, the show is impenetrable if not watched from the beginning. The style of the show, the dialogue, the motivations of characters, the atmosphere, the meaning of much of the abstract symbolism, and the progression of the plot is not, in any way, suitable to a new viewer who begins at any point. To understand the show, remotely, you need to see from the very beginning, because any other way there is no real way you can pick up the show and have any level of understanding for what's happening, or tolerance/love of the show's stylistic choices. The only course for the show is that it sheds viewers from the beginning, as they gradually feel that no longer can deal with a certain aspect of the show. While people may suggest that it could pick up viewers who binge watch the show, this is problematic in many ways, because binge-watching the show is an entirely different experience to watching it on a weekly basis, and considerably alters the pace (this is no clearer in season one, when one's perception of Will's arc is completely different when watched over the course of many weeks) or one's appreciation of the pace (it may have seemed fast paced when binge watched, as Breaking Bad did when watched in rapid pace, but it is another matter entirely watched weekly).
EDIT: Also, advertisements really interrupt the flow of the show and the atmosphere it works hard in creating. I wouldn't be surprised if many people didn't watch the show live and watched it after having recorded it do that they could skip past the advertisements.
Now, could NBC's marketing have done a better job? Perhaps. This was never a show however which would have mass appeal, there are too many barriers to so many people, and it's told in such an alien way that even those who may typically enjoy shows produced at a high quality may be repelled from it (at the very least may be repelled from watching it on a week-by-week basis). Perhaps on HBO it could have survived off the niche appeal it has due to the stylistic choices that have been made, but there was no way that NBC could ever market the show in such a way that it would appeal to a mass audience in spite of its high quality; as soon as people turned on the show without having watched previous seasons they'd change the channel.
EDIT: In short, it's just a very hard sell, and a very tough show to convince people to stick with, particularly as it becomes increasingly abstract and symbolic.