It says something about the kind of year Kanye West's had that his claim to be "the World's No 1 Rock Star" was relatively easy to miss. What price a bit of self-aggrandisment no different from the claims of dozens of hopeless Britpoppers to be "the best band in the world", when set next to the other stuff he's said in 2013? There was the interview with the New York Times, in which he announced that "the world would win" if only more people would "respect my trendsetting abilities", then variously compared himself not merely to Gil Scott Heron and Miles Davis, but Le Corbusier, Steve Jobs, Walt Disney, Henry Ford, Nicolas Ghesquière (the creative designer of Louis Vuitton), Anna Wintour and David Stern. It wasn't 100% clear if by the latter he meant David Stern the artist, David Stern the commissioner of the National Basketball Association or indeed David E. Stern, voted the 22nd most influential rabbi in America by Newsweek magazine in 2011, although given the tenor of the interview, you wouldn't bet against him meaning all three of them. There was the interview with Radio 1's Zane Lowe, which succeeded in making the normally irrepressible DJ sound like the voice of calmness and reason, as he gently suggested West might consider some formal training before moving into the field of architecture, the rapper's self-proclaimed similarity to Gaudi notwithstanding. West, meanwhile, proffered the intriguing notion that the only possible response to any of his creative endeavours in any field of the arts was to thank him "for making civilisation better". And then there was the interview on Eminem's Sirius XM radio station in which he appeared to go completely bananas. At one juncture, he yelled at the interviewer: "I'm standing back and telling you I AM WARHOL! I AM THE NO 1 MOST IMPACTFUL ARTIST OF OUR GENERATION. I AM SHAKESPEARE IN THE FLESH!", but it wasn't all as bashful and self-effacing as that.

Indeed, if we mentioned every one of Kanye West's extravagant claims over the last 12 months, we'd be here all day. (We haven't even touched on the interview with Philadelphia's Hot 107.9, in which he appeared to suggest he was more important than President Barack Obama.) Suffice to say that when a satirical website ran a spoof news story reporting that West had suggested he was "the next Nelson Mandela", thousands of people, including one South African daily newspaper, took it seriously. The parody just didn't seem that far-fetched, particularly if you took into account his line on Blood on the Leaves, a track from his most recent album Yeezus, that claimed he was a victim of "apartheid" because he'd once been forced to seat his partner and a "second-string" girlfriend in different sections of a basketball arena ("the injustice of apartheid is nothing like separating one's wife and mistress at a basketball game," offered the self-styled "hip-hop Wikipedia" rap genius, for the benefit of anyone tending to think West might have a point).

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But when it comes to his claim to be the world's No 1 rock star, it's hard not to think that West might well have a point, assuming the ideal rock star is someone provocative, complex, remote, strange, fascinating, outrageous, unpredictable, infuriating, ridiculous and willing to push at their own musical boundaries. It seems fairly safe to say it is – no one ever fell for the myth of a legendary rock star because they seemed so eminently sensible, conventional and grounded – and equally safe to say those kind of rock stars are in desperately short supply these days. There have been lots of theories posited as to why, some more convincing than others: everything from a desire to avoid inflaming social media's penchant for indignation and outrage, to a tendency by record companies to play it safe in an uncertain climate, to the rise of colleges and other institutions that try to teach people how to become pop stars, an area that was once wide open to the intuitive and autodidactic. But whatever the reason, rock bands in particular seem to be getting gradually more anonymous: in the UK, the year's big breakthrough guitar acts were Bastille, the Lumineers, the singer-songwriter Passenger and Imagine Dragons, none of whom are selling albums on the basis of their fathomless charisma and gripping unpredictability.

Kanye West, on the other hand, ticks all the boxes. He's certainly provocative, and not merely because he keeps bellowing at radio presenters about his manifold similarities to Shakespeare or Gaudi: the merchandise for his most recent tour was based around the racially-charged symbol of the Confederate flag. He's certainly pushing at his own musical boundaries: whatever you make of Yeezus' lyrical content – and it's a doughty soul indeed who attempts to argue that it isn't, at the very least, hopelessly contradictory – in purely sonic terms, it's audibly the most radical and challenging album that any star of West's commercial stature has made this year. He's got ridiculous grandiosity and a certain remoteness from everyday life down pat: this is, after all, a man who proposed to his fiancé by hiring a 45,500-capacity sports stadium and a 50-piece orchestra, who appears on stage rapping from the top of a mountain and conducting a dialogue with a man dressed as Jesus. ("Oh shit! I can't believe it!" offered West when the messiah took the stage.)

And he is genuinely fascinating. Attempts to explain his public behaviour in 2013 have ranged from, at one extreme, the suggestion that he's having some kind of nervous breakdown to, at the other, the belief that he's a maverick voice speaking truth to power about race and art. Somewhere inbetween lie the theories that he's either a brilliant manipulator of the media – he's certainly omnipresent in the headlines – or a petulant little berk throwing a strop because fashionistas didn't like the leather jogging pants he designed. And as anyone who's watched Mick Jagger act or read Billy Corgan's poetry or indeed seen the computer art of Ringo Starr will tell you, he's not the first person to believe that selling a lot of records automatically confers upon you the status of polymath genius, but he's certainly the most vociferous and unrelenting in his claims to that title. But however tempting the urge to just dismiss West as a narcissistic crank or a nutcase, there's something weirdly compelling about him, perhaps because there's frequently a germ of truth to what he says, even if you have to delve through several leagues of demented-sounding solipsistic old cobblers to reach it. It's perhaps erring on the reckless side to claim, as West has done, that anyone who dares to suggest he might be a better rapper than a fashion designer is a bigot, or to demand a global boycott of Louis Vuitton products because the company's vice-president declined to meet him (maybe he just didn't fancy being subjected to a monologue about Kanye West's similarities to a variety of legendary artists, film makers and designers), but equally, it's hard not to notice that there are virtually no black faces in the world of haute couture, other than on the catwalks. There's something faintly pathetic about his motivation for writing Yeezus' I Am a God – apparently he was cross because designer Hedi Slimane attempted to secure West's exclusive presence at one of his shows – but something intriguing about his point that if he'd called the song I Am a Nigger or I Am a Gangster or I Am a Pimp, no one would have flinched.

There may even be a tiny grain of truth to his constant claims of selflessness: "I'm doing this for you," he recently told one audience during one of his regular onstage rants (or, as he prefers to have them described, "motivational speeches"). It has to be said, it seems a little improbable that West is motivated by altruism, but there's certainly a positive side-effect of his behavior for everyone else. It would be as crazy as he sometimes appears to be to suggest West should be given an easy ride: what he says and does should be interrogated, argued over, mocked. But we should understand that if he took his loudest detractors' advice and just shut up, then the world of pop would immediately become a less interesting place, because, almost uniquely at the moment, Kanye West seems to have an innate understanding of what it takes to be a great rock star. Long may he rant. Or, rather, deliver "motivational speeches".

• Read Paul MacInnes on Yeezus, our No 1 album of 2013

• See all our Best Albums of 2013 coverage here