I find it interesting the difference between Sherlock Holmes and the image of him in the public consciousness. It isn't like any other character where they might have a slightly different personality in the novel than in the films, the gap here is so wide they are almost entirely different people.
They have a different appearance (he never wore that hat), a different personality (Sherlock is NOT actually rude or abrasive), different catchphrases (he never says 'the line'), and completely invented dynamics between Irene Adler and Moriarty. (Moriarty was just a plot device and Adler was never a love interest.)
BBC Sherlock Holmes has more in common with Sheldon Cooper than he does with the original character, to the point he would most likely be completely unrecognizable if you changed his name to David or something.
That's what gets me about BBC Sherlock. Think about it. Truly, genuinely think about it for a moment. If you renamed that version of Sherlock to Robert, what would you actually truly honest to goodness have to recognize him as Sherlock Holmes? Very little.
Is this necessarily a problem? I would say no, as it was inevitable that this happened. The character has been around for almost 140 years. Every attempt we make to adapt the character further distances him from us, even when we try to write pastiche novels.
But if it is inevitable, is it fair to judge the modern interpretations of the character in comparison to the original stories? After all, it would be like judging a son for not wearing a powdered wig like his great great great great great great great grandfather.
What does it mean to write a good Sherlock Holmes story if the character and his world is always evolving over time?
The iconography of Victorian London is a core part of his character within pop culture, which is only true because of contemporary audiences.
At the time, Victorian London was the modern day and therefore carried no significance, but today it is difficult to separate him from that era no matter how hard one may try.
So the question remains; what is to be done? To answer what makes a good Sherlock Holmes story, I would suggest one would have to determine which Sherlock Holmes they are referring to.
For pop culture, Sherlock must be a period piece because that is the context with which people around the world have come to love him.
For the original stories, there is nothing preventing him from being modernized because at the time of his creation, he was a modern man.
To be faithful to the Victorian Sherlock might actually involve reinventing him for the modern day, as paradoxical as that may sound. He was intended to be a man of the future, a man who used advanced technology living in the modern day.
You were intended to marvel at his genius! He was flirting with concepts like forensic science that we wouldn't even have a name for until years later. It is hard to be impressed by a man who didn't know the earth revolved around the sun.
Therefore, to write a truly faithful Sherlock Holmes is to write a man of the 2050s in 2026.