I think the first premise is correct, that Sherlock Holmes' survival as a popular fictional character (which is unique in the last 100 years, as far as I can remember – I read an article once which compared him to Robin Hood and Tarzan, but that was written before they had pretty much vanished from popular entertainment) is at least partly based on how little we know about him, past the obvious catch phrases and accessories.
Contrast him with Nero Wolfe, for example. Nero Wolfe was (no pun intended) very well fleshed out as a character. If you read all of the novels and stories, you knew his history, his beliefs (quick, what were Holmes' politics?), his enthusiasms, and his phobias. You knew his quirks, and you could also infer the reasons behind them. So, Wolfe is not (so to speak) very flexible. You can't make him into an action character or a ladies man or an international man of mystery.
So, I think that's true, but I disagree with the second premise, which is that Holmes is so sketchily described because Arthur Conan Doyle was not a good writer. I am not, I should explain, leaping to Doyle's defense because I'm a Doyle fanatic (or a Holmes fanatic). As I talk about here and here, Jan Sleet is obviously a big Holmes fan, but I'm not. I've read the stories, I've enjoyed the Jeremy Brett series of television, but I'm far more enthusiastic about Nero Wolfe, for example.
But I disagree with the premise that good writers are the ones who describe more about their characters, and bad writers create sketchy characters with little depth. As Orson Welles pointed out, it is a sentimental 20th century idea, the legacy of psychoanalysis (which he hated), that the more you know about fictional characters the better the writing is.
He would use the example of Iago, and the fact that there is no explanation offered in Othello for what a shit Iago is. People in this era are not comfortable with this, and want a psychological explanation, but (as Welles pointed out) anybody who has been around at all in the world has met people who are just rotten (he said it better, but you get the idea).
Oh, okay, I looked it up. He said about Iago, "The great criticism through all the years has been that he's an unmotivated villain, but I think there are a lot of people who perpetuate villainy without any motive other than the exercise of mischief and the enjoyment of the power to destroy. I've known a lot of Iagos in my life. I think it's a great mistake to motivate it beyond what is inherent in the action."
There is more than one way to write well. Not all good writing is the same. Is David Lynch a bad movie director and writer because his characters have pretty much no psychological depth at all? Of course not, because he's doing something very different.
Also, it just occurred to me that my defense of Doyle is clearly not self-serving, since I am the opposite. You want to know about Jan Sleet's parents, her family, her upbringing, how she was in high school and college, where she was before U-town, and where she goes afterwards? It's all there. Why does she travel the world with Marshall as her platonic assistant, and then turn around to seduce and marry him? What is she like in bed? Does she ever cry? It's all there.
Was Doyle a great writer? No, I don't think so. Stout was better, for example. But Doyle created Sherlock Holmes, who has survived quite nicely into the 21st century, and he created a template that many thousands of writers have used since. For one example, why does Marshall narrate the mysteries, when he mostly doesn't narrate the novels? Well, mostly because Archie Goodwin narrated the Nero Wolfe stories, and that was because of Holmes and Watson. That's just one example of many.
I also read an article once where it pointed out that one of Doyle's greatest techniques was his ability to nest flashbacks within flashbacks, stories within stories, so that a lot of story can be told in comparatively few words. Watson tells you the story, then a client arrives and begins to tell a story within Watson's story, and sometimes there's a further flashback within that story. The story construction itself is very much like a puzzle box.
Detective story writers, whether they are aware of it or not, follow what Doyle did the same way movie directors are influenced by Ford, even if they've never seen a Ford picture. By which I don't mean to compare Doyle to Ford in terms of skill, but I think it's too facile to write him off because of his supposed weaknesses, without taking into account what he did create and the influence it had (and continues to have).