You can find a detailed biography of Sir Arthur Conan Doyle here and a shorter one here.
Illustration of the short story A Scandal in Bohemia, which appeared in The Strand Magazine in July, 1891. This illustration appeared on page 65, and is captioned "HE TORE THE MASK FROM HIS FACE." (Source: Wikipedia)
Leaving aside the fact that Conan Doyle did write two later stories from Holmes's perspective, how do you imagine a mystery tale written by Holmes would look? What would it emphasize? If he narrated, say, "A Scandal in Bohemia," how would he describe his own feelings for Irene Adler (if at all)?
Irene Adler has to disguise herself as a man to get the drop on Holmes; her past as an actress gives her mobility that, for example, a working class woman like Mary Sutherland lacks. What would it take for a woman in the 1880s to be a practicing private detective like Holmes? Or could a lady even do so at all within the Victorian London that Conan Doyle presents?
Watson keeps telling us that Holmes is unique, and as such, it's hard to imagine him being part of anything so conventional as, say, a family. Eventually, Conan Doyle does invent a brother for Holmes, Mycroft, who is even more observant and wily than Sherlock, but who is immensely lazy. What kind of family could have produced two such unusual children? Is there any model of education going on in these stories? How does Holmes learn what he needs to know to do his job well?
Watson's ability to observe Holmes seems to depend on their cordial, bromantic friendship. How would the story's narrative structure change if Holmes were to form a romantic attachment with someone? Would it need to change at all?