On the Mac I don't mind having Music, iTunes Music Store, and Apple Music all in one app. However ideally I'd rather have one app that manages my music library (both local and cloud) and one app that manages pulling content into the library. (Similar to how the iTunes and Music apps worked on iOS before Apple Music.)
The problem right now seems to be that they don't want users to think too much about organizing their collection. Just have the stuff you like, pick what you feel like listening to and don't worry about where it is. Which would work if we always had an internet connection, or if we wanted to waste our bandwidth on that.
Personally I planned on paying for Apple Music when it launched ... and then had it utterly destroy my Library. (I can't exaggerate how beyond repair it was. I had to dump the whole thing and restore from Time Machine, I couldn't even use Apple Music on my phone because it refused to download all of the content I wanted to have. Which makes no sense. I have a 64 gig iPhone, I don't want to waste my limited data plan and battery constantly downloading music I've already listened to before!
On the Mac there should be for Music:
Music: which handles local content, allows streaming content that is non local, and makes accessible purchased content from the iTMS.
iTunes: which handles purchasing content and selecting new streaming content to be added to your library. (And yes there is an inelegance to having streaming and content that's only available to purchase in the same app. Blame the labels for that. They can easy show when someone isn't subscribed to Apple Music "this would be free included in an Apple Music Subscription" and they can also show to subscribers when an album is not yet available as part of their subscription.
On the Mac for video:
iFlicks: (Knowing Apple they'd call it iTunes for Video) This would allow you to purchase movies and TV shows from Apple (not sure how big of a business this is for them these days) and when you'd go to play it it would automatically launch ...
Movies, FrontRow, Theatre whatever you wanna call it. Which would be like iTunes but for movies (and recognize that movies aren't tunes so having them be in an app for tunes is stupid) Here you could sort movies by release date, genre etc. You could also (gasp) access content from Netflix and other VOD services that could integrate, and all the login info would be stored in iCloud so that when you buy an Apple TV the info only requires a single sign on.
They could probably even just allow developers to put in modified versions of their iOS apps compiled for whatever processors Apple's running at the time.
For Apps, just use the Mac App Store if you want to have local copies on the computer ... not sure why we even still have that?
For Books, have iBooks and Bookshelf. In each app you could have a button in the corner that automatically launches it's companion app. But these apps have all gotten so bloated. Each one loads up it's own store, and half the time I end up clicking on the wrong thing and ending up having the iTunes Store interface loading and it's a gross experience.
Oh, also the Video app would allow for not JUST mp4s and streaming content, but also AVI and MKV video files. Because ... WHY THE HELL NOT APPLE!? WHY THE HELL NOT!? (Also allow for storing libraries on a NAS.