I think the strongest real-world case is El Sistema in Venezuela: free ensemble music in public settings gave low-income students structure, focus, and a reason to attend school. That is the core case for mandating music education. If it is optional, access collapses to schools with money and parents who can pay. A mandate sets a floor: every public school student gets sequential instruction in rhythm, pitch, and collaboration, which supports math and literacy and builds persistence. Cost and scheduling are real constraints, but they are implementation problems, not reasons to deny the baseline to everyone.

Your tradeoff is real but you misidentify what the mandate displaces. The actual choice isn't music versus math. It's mandatory music versus music that only exists where parents can pay. Make it optional and schools under budget pressure cut it first, so access tracks zip codes, not interest. A single weekly period is a rounding error against the years of students who never get the option at all. Your position says let those who want it choose, but choice means nothing if the option was never offered. The mandate is the only mechanism that holds that floor up.

Offer without require isn't a floor, it's a suggestion. An elective carries no accountability: a school can list music, staff it with one part-time teacher, and never actually schedule it into a student's day. The mandate is what makes availability real and checkable. Your hollow seat time worry is a quality argument, and it applies equally to a badly taught math class, so it can't single out music. Fund and staff it properly, yes. But the requirement is the only thing that stops budget pressure from quietly deleting the option altogether.