Though primarily a comedy show with the mystery element taking an increasingly tinier backseat, Monk actually makes a quite serious point about the Great Detective figure, namely the apparent impossibility of being both a supermind and a normal being with a normal life. Adrian Monk at the end of the day is not substantially different from glorious predecessors such as Sherlock Holmes, Nero Wolfe or Philo Vance. Alike them, he is basically an eccentric loner with hard-working grey cells but comparatively poor social skills. What makes him, unlike them, a comedic, and occasionnaly tragic, figure is that he's lost control. Great Detectives from the past were defined by their quirks; Monk on the other hand is dominated by his.
Despite a popular conception fueled by lazy scholarship, a Great Detective is not necessarily a flamboyant individual ridden with eccentricities: think of Miss Marple, Commissaire Maigret, Uncle Abner, Father Brown, Anthony Gethryn or Ellery Queen's later incarnations. Still, that particular brand of sleuths has long been predominant and starting with the father of them all, C. Auguste Dupin, gave the genre some of his most memorable and recognizable characters. But isn't "eccentricity" rather mild a word to describe the aforementioned Chevalier's love of night for its own sake which prompts him and his anonymous friend to literally live into obscurity? "At the first dawn of the morning we closed all the messy shutters of our old building; lighting a couple of tapers which,strongly perfumed, threw out only the ghastliest and feeblest of rays. By the aid of these we then busied our souls in dreams -reading, writing, or conversing, until warned by the clock of the advent of the true Darkness."* The narrator readily admits that "had the routine of our life at this place been known to the world, we should have been regarded as madmen - although, perhaps, as madmen of a harmless nature."*
This would apply just fine to many of Dupin's followers, though the actual harmlessness of some - one Sherlock Holmes comes to mind - is questionable. Maybe Monk isn't the first mentally-disordered detective; he's just the first to be diagnosed as such.
He is also the first to be seriously impaired. Hercule Poirot may have been every bit as obsessive-compulsive in his own way as Monk, but he was able to function in an admittedly limited yet autonomous way. His relationship with Hastings was one of condescensive friendship, not dependance, as evidenced by the fact that he didn't seek a replacement when the good captain went off. Monk, on the other hand, relies on his assistants; he needs them even in the most trivial aspects of everyday life, blurring the usual Holmes/Watson hierarchy. Monk's intellect doesn't make him a superior being, and is closely related to his disorder, so much so as it is hard to see which one proceeds from the other. In season 3 episode Mr. Monk Takes His Medicine, a change in Monk's treatment removes both his OCD... and his deductive skills.
Is some sort of mental illness a prerequisite for being a Great Detective?
This is a fascinating question indeed, which Monk's writers are to be commanded for asking, even unwillingly.