@ artie-
As you surmised, it probably would be difficult for your son to get into a performance program given where he is, both jazz and classical programs will be extremely competitive. As others have suggested, there is the possibility of going the BA route and/or dual major that way. This way he can pursue music and see if in fact he really wants to do it, while having the flexibility of a dual major and/or switching majors and so forth.
As far as teaching goes, music ed degrees are aimed at people wanting to teach in the public schools, they take a wide range of things, they have to learn about the various instruments to be able to teach them, plus they take general education courses the way other types of teachers do. If your son is thinking he might want to teach privately, or perhaps teach let’s say guitar at a music school or maybe even a private school, he doesn’t need an ed degree (obviously, if he was going to be a music teacher in a private school where he is expected to direct the school band/orchestra, or teach multiple instruments, similar to what a public school music teacher would do, then he would need that experience, but I meant simply if let’s say he was going to teach guitar to students at a private school).
Given he is coming into this late, the BA approach sounds reasonable to me as a way to get his feet wet without cementing anything.