It's another of those examples of Starfleet & 24th century humanity being so advanced that their training covers an almost absurdly wide ranging number of fields. Engineering, astrophysics, biology, assorted other sciences, diplomacy, law, military & combat tactics, the history of countless cultures & I'm probably forgetting some. Hell, if you go into medicine, and end up commanding a Starship like the Pasteur, I imagine you have to know everything about everything. How some of these people had spare time to learn to play a musical instrument, even as just a hobby, is totally beyond me
This made me LOL. But I don't think its just their training. You are thinking like a member of the 21st century here on earth, where the primary day to day goal/necessity for most (civilized) people is to make MONEY. And for 99.9% of us that means working a job where you pretty much do the same or similar things every day. When you take that out of the equation who knows what you could actually accomplish. I know if I had been a billionaire at age 20 I would have done a LOT of stuff and learned a lot about different cultures. Even a lot of wealthy people continue doing the same thing (running the same company, etc) for the rest of their lives just to make more money, though I will never understand why. Anyway now we're way off topic.