Elementary has been described by critics as a subversive approach to the Holmes canon, but its unorthodox nature has many purists up in arms about its casting, setting, and procedural format. However, the show has a complex relationship with its audience in how it treats them. More favourable critics often mention how it plays with old narrative devices found not only in the books themselves but also in its adaptations. So, let's examine this, shall we? Unmarked spoilers below.
Several canon purists refuse to see the merit in this show - and some refuse to acknowledge it as an adaptation altogether - because it's so far gone from the original canon; but that may be the whole point. Adaptations have used and reused ACD's old tropes and worn them out to the point of exhaustion. Brilliant white men solving crime, disregarding the rules of lesser mortals simply by the virtue that they are brilliant. He is, after all, the archetype many Great Detectives are based upon, from Monk to Batman to Detective Conan.
In comparison, this Sherlock Holmes is no less canon than The BBC's Anti-Hero with a god-complex note , or Hayao Miyazaki's crime-solving dogs, or Guy Ritchie's guile action hero. Yet, setting it in New York City rather than Victorian London has somehow forever tainted the canon beyond recognition.
Joan, as an Asian woman, former surgeon, former sober companion and novice detective, is often underestimated personally and professionally by the show's characters, Sherlock itself (in the beginning), the NYPD, her family and friends and the antagonists of the week. In response to that, she has self-esteem issues and is unsure of her own abilities when she is often right. Moriarty, ignoring her importance and her intelligence, understimates her as well, even calling her a 'mascot'. The Dramatic Irony of it al is that Joan is the only one who was able to understand Moriarty's motivations and create a plan to capture her.
The 'mascot' comment is also a nod to how often people of color are reduced to Token Minority; just see the Magical Negro and Magical Asian tropes. They exist on the sidelines to help the hero along, but rarely have enough motive, backstory or agency to actually participate in the plot; this gives Joan's defeat of Moriarty so much more poetic satisfaction. More than that, the show counts on Joan being underestimated. Just like every episode has an overlooked minor character who turns out to be the murderer, the audience isn't supposed to see Joan's victory coming either.
Irene Adler and Moriarty
In terms of narrative device, I'm keeping these two characters separate. The first notable character to mention is Irene Adler, and how her storyline is handled; she is, after all, the catalysis for the plot, the ghost lingering throughout season one. She starts off as a Stuffed in the Fridge Posthumous Character, with her only relevance to the story reduced to add some backstory mystery and give Sherlock something to angst about. Then in the course of two episodes she's found alive, but very broken, then an agent of Moriarty, then it turns out she is Moriarty. Irene's character not only exploits and deconstructs the Stuffed in the Fridge trope, she weaponises it. She exploits Sherlock's heroic angst for all its worth, setting him on a wild goose chase on M and removing him as an obstacle in one go. This is a brilliant way to turn a rather cheap and overused storytelling device on its head and subvert it - especially as most victims on the trope's page are women, who have to die to trigger the (often white, often male) hero's angst. But just like Moriarty well-crafted grift, the show conned us along with Sherlock into believing in this trope.
This leads us to the Gender Flip and Composite Character or Moriarty/Adler. The struggle between Moriarty and Holmes is another tale of the battle of wits between super-intelligent white men, with women's bodies littered around them. In the 2009 films and the BBC series, Irene is robbed of her agency. She becomes a chesspiece for Moriarty and both Adlers are ultimately beat by their feeling for Sherlock. This Moriarty sees her beat, again, by her feelings - but not by Sherlock. Her love for Sherlock and Sherlock's love for her puts them into a stalemate. It is Joan Watson who claims the ultimate victory over Moriarty.
Now, for the other side of the fourth wall. While the show appeals to a Periphery Demographic, many of its most passionate fans have been in fandom for long time themselves, enough to see old tropes rehashed time and time again. They're also well-versed enough in Audience Reaction and Characters as Device that Elementary's subversive storytelling comes as a pleasant surprise.Elementary has been compared to an AU fanfic, born from the desire to see a more of a diverse, progressive representation.
Like many Watsons before and many Watsons after, Joan acts as an Audience Surrogate. But instead of assuming the audience are all straight, white men, she is the audience stand in for women, feminists and people of colour. She calls Sherlock on his bullshit, she doesn't hold him up on a pedestal, she grows to respect him, but does not worship him. As Joan and Sherlock's relationship matures and evolves, the audience's loyalty is earned steadily over the season, through building up a strong friendship and positive representation; its feminist themes, diverse characters and valuing character development doesn't hurt.