Here we have a motif straight out of crackfic, the musical episode. Yet the author uses this setting to explore some very serious issues -- it's actually a story about attachment problems told through the metaphor of musical interaction or rejection. Touch on another Sherlock motif, and what you have is fantastic analog of asexuality: a situation in which Sherlock doesn't want to do the thing that everyone else is doing, and people think less of him for not liking it and not understanding why it's So Very Important to them. There's quite a lot of astute exploration into how social ties form between couples or work groups, and how that gets expressed.
This story reminds me strongly of "Once More, with Feeling." That famous episode of Buffy the Vampire Slayer showed the problems that can come from stripping away filters and forcing people to sing about their feelings. In that show, they're not used to it, because it's not natural; it's demonic influence. Compare that with the above story set in a world where musical interactions are the norm.
Another variation is Happy Feet, in which all penguins are expected to sing, and the one who can't gets rejected.
There is a lot of potential to explore more challenges caused by living in a musical world. Most musicals never examine the fact that they are musicals. They just do their thing, a quirky little commentary on everyday life. But when they become genre-savvy, a whole new realm of possibilities opens up. How does the musicality work? What can go wrong with it? How do people cope with disabilities -- being deaf, blind, mobility-impaired, etc. in a world where singing and dancing are fundamental aspects of every human interaction?
I'm not all that fond of musicals, but I'm fascinated by the "musical world" as an AU setting template.