Some schools have specific distinctions of “general music” which I’m interpreting to probably be musicology (music history, theory-related content). Music composition is helpful to those who want to study composition and depending on school to school: can be super selective and competitive, or more open to a lot of students.
Also most composition majors, usually have to take some type of theory/history as well that is in compliance with their degree requirement so even if your son is not going in as a musicology major, he would be required to take musicology-related courses such as theory and history.
That being said you are correct though. On paper: it isn’t necessary to get a music composition degree as an undergrad.
However, schools with an undergrad music composition program offer him the ability to get a head start on having access to courses that is specific to music composition during his 4yrs at college/uni. Certain schools with strong composition programs also allow your son to work with top-class educators in the field and access recommendations for an even stronger grad program.
But given that he’s attempting to dual major: definitely he should carefully consider what he expects his college life to look in order to make decisions about a school or major first.
Composition is always something you can do on the side even if you never get a degree for it. But getting into the academic school system side of it: needs preparation and running the gymnastics of applications like any other major.
Definitely keep doing contests and keep composing even as an undergrad if he has plans to do composition in grad school instead: because by grad school-- most schools want a portfolio proof that you compose and have skill and knowledge of it.
In the case that your son isn’t totally sure about double majoring: definitely pick a school with an option of the Comp Sci degree and music composition department-- not just musicology. And studying music composition usually has musicology-centric classes in it anyways!