From what I've seen, there are a couple of things that are linked to higher IQ's. One of them is knowing multiple languages, and the other is being able to play a musical instrument. I know that a lot of (pre-college) schools out there are already requiring a second language in order to advance, and maybe learning a musical instrument should be another thing that is required.
However, it's easy for me to say this because I graduated High School a while ago. When I WAS in High School you had to take a second language (mine was Spanish). Personally, I'm terrible at learning second languages. I've tried on multiple occasions and have not done very well. I was only able to pass Spanish because my teacher was not very good and mostly passed everyone.
Still, in Grade School every student at the school I went to was required to learn how to play the recorder. I was okay at it, but if I picked one up today (almost 20 years later) I would barely know which end to blow (insert joke here). I can imagine that there are many students out there that simply wouldn't be able to do well in music classes... and for them I don't know what the alternative would be.
The only alternative I can think of is that a music class for Grade School and High School could be a pass/fail class that wouldn't impact the students GPA, and if a student simply is not able to do well in a music class then perhaps there can be another class they can take instead. This could create several other problems, but it might be something to consider.
TL;DR - I think it's an interesting idea that could potentially lead to smarter students, but not all students will excel at this so maybe it shouldn't be required. Still, leaning yes on it being a requirement.