I think the reason is because Apple doesn't use the "hamburger" menu...
Apple doesn't use the Hamburger button because they don't use it anywhere else in their iOS apps. The use the bottom row of icons pretty much everywhere. That was their choice and I'm fine with it.
My initial confusion with Apple Music was the dramatic change in those icons. Moving most of what was there into the My Music tab in the lint/button in the middle of the screen.
Also, iTunes may be a huge resource hog, but it works and displays all your music in one place. Not a section for locally stored music vrs. music on the service's servers. I was OK with Spotify until I realized that the music I had stored on the HDD was completely separate from the rest of the music displayed on the client. Amazon's client is so clunky that it's pretty much useless. Amazon is a great way to store your music offsite in case you loose your local storage. Like I did about 2 months ago. Thanks to that crash, all the music I had access to was on my iPhone and stored on Amazon's servers.
Hopefully, Apple will see fit to display more that 25 albums within the artist's pages, then I think it will be pretty much perfect.
One thing they should really do (and maybe they did and I just flew past it) is show some screens when users first turn on Apple Music to teach them the difference between locally stored music, iTunes Music Library music and Apple Music. That would really help people understand what has happened to the app.