Didn't Apple at one point also deny apps that replicated/repeated builtin functionality? I think the restrictions are a lot looser now but maybe that's why no one's put much effort in?

Specifically for a music app, it would probably have to somehow link in with files synced by iTunes, which may be difficult. As compared with Android where music apps can usually just be pointed to an eMMC/SD card location which can be easily written to with just the raw files straight from your NAS or wherever.