Sure, costly signaling has to be a big part of any analysis, but isn't sports also a costly and unproductive way of signaling one's physical and genetic fitness? Sports can also be a fun way of exercising, but some kids find ballet fun and it can also be good exercise. People have claimed various (non-signaling) benefits of learning to play an instrument as well, and that can also be an enjoyable activity for some.
Apparently some parents make their kids take lessons to increase the chances of getting into private school, and eventually an elite college, so another big part of the analysis might be the costs/benefits of private vs public school and elite vs non-elite colleges. (I personally went to public school and a state university.) Another big part is, if you leave a kid a lot of free time, how likely is it they'll eventually find something valuable to do with it? Or alternatively, what are some more valuable activities we should try to guide a child into instead of the standard ones?
Disclaimer: US-centric perspective
Elite colleges generally students who are "genuinely" (insert adjectives here), not yet another honor roll student with a boring essay about how their voluntourism trip to Africa changed their life. In a competitive field like that, you want to stand out, and you stand out a lot more by doing something that both clearly signals being good at things and is different from the signals that other students are sending.
Therefore, doing whatever other students of your socio-economic status do is a bad strategy. Much better to do something impressive and different.
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