If an OS update only changes something that has no interdependencies (eg, changing an icon), you don't need regression testing. If the 'Music' app on iOS would be updated on its own, Apple would only be able to improve the parts of it that have no interdependencies with the rest of the OS.
The problem is that you cannot separate the Music app from the OS because it integrates with the 'music' library which is part of the OS. And I am pretty sure it also uses non-public APIs (or just new APIs which are still non-public) for all the synching going on in the background with the iCloud representation of your music library. And those APIs might be used by other Apple apps (eg, iBooks).
Asking for Music to be a separate app is asking for to develop sync services for this app only (as third-party apps have to do). I don't think that is an efficient way for Apple to write software.