I've often thought this...

Just ran across an article suggesting that a few years of music lessons when you are young confers mental benefits for many years after:

research has linked the kinds of brain signals seen in those with musical training to heightened auditory perception, better auditory-based communication skills and improved executive function. The last of these — executive function — encompasses such key learning skills as attention, organization, short-term memory and reasoning.

The wording of that is foggy about whether it is causation or mere correlation, but that is true of a lot of this kind of research. Still, it takes a lot of discipline to learn music properly, to develop rhythmic precision, the ability to phrase, the ability to memorize pieces, the ability to listen carefully to what you are doing. I don't know of another area of study that so intimately connects abstract mental function with physical control. Purely academic studies don't and neither do sports, as each focuses on one half of the equation.