I have iOS 9.2 and updated Music to the latest version. There is no "view all songs". But perhaps you found some way? Like I just want to see all songs, not playlists, not genres, everything. I'd love to find out :)

Go to "my music" and where it says "Artists" (it's pink) with the downward carrot, press it - you'll get a list where "songs" is an item.

The reason you couldn't figure it out is because Apple has completely abandoned usability in favor of a comically flat UI aesthetic.

Wow. Many thanks! Such a dumb UI decision.

I'm constantly re-discovering functionality hidden behind buttons that don't look like buttons in iOS.

My Music > Tap the red "Artists" button beneath the scrolling list of recent songs at the top.

A UI disaster that most Music users will never discover.