It's not consistent across devices, it's consistent within the behaviour on a specific skin. The skins are there to provide different behaviours for the UI so you can choose one you like. The phone skin in particular is designed to be used on small touch screens, therefore it uses a different operating paradigm - one without 'drop-down triangles'.
It is a touch-oriented UI. Therefore to enter a menu one must click on the title for that menu. If you notice, the behaviour is the same for Albums, Directories, Radio Stations, and Playlists - clicking on them all enters a menu, whereas in Desktop clicking on them adds them to the play queue. That's how the phone skin is supposed to work.
In the phone skin, click on the playlist like you describe to 'enter into the playlist'. 'Play All' is right there at the top under the playlist name, above the list of tracks. This exists on the phone skin, and the phone skin only, precisely because the skin behaves in a different way from desktop.
If you want a skin on your phone that behaves the same as the desktop skin, use Tablet, that's what it is for. Tablet skin in 1.15 is identical to Phone skin in 1.10. I simply renamed it, there have been no changes to the way it works.
Also remember that you must switch CD player mode to ON in every browser on every device you use - it is not a global setting. The behaviour you are describing for the phone skin sounds like what it would do with CD Player mode OFF