I’ll agree, however, that music is an essential part of human cultural heritage, and every person should be given the chance to learn to play an instrument. Just as every person should at least a little bit learn how to cook, and to sing, and to dance, and to juggle, and to sew, and to program computers, and to write mathematical proofs, and to build wooden furniture, etc...
I think the great-grandparent poster was talking about something different though. Not teaching a child to play an instrument for a year or two to delight in music’s intrinsic value and then optionally continuing it if the child expresses interest, but ramming rigorous lessons down a child’s throat, forcing the child to spend years in training that he or she thinks is boring or a waste of time.
As someone who ran D1 track & field yet can also play Liszt's Transcendental Étude No. 10, I would have to disagree with you. I think that running has had a much deeper impact on my physical and mental development than the process of slowly refining a niche skill.
The ability the play the instrument is not nearly as valuable as the experience in learning, improving, and using your brain in ways that doesn't involve math and reading.