There's a risk of using status considerations as a hammer against which everything looks like a nail, but in this context I really do think they're pretty often the right answer. Amy Chua, for example, wasn't forcing her daughters to learn violin or piano (and only those instruments, IIRC) primarily because it builds some vague form of character; she was doing it, consciously or not, because violin and piano are coded as upper-class instruments and learning them is a form of costly signaling. Contrast, say, guitar; becoming a competent guitarist isn't much easier than becoming a competent pianist (I tried both when I was younger, without much success), and any cognitive effects from learning it must be much the same, but it lacks the desired class and personality associations.