So I've been reading a lot of these replies and NONE have been helpful. However, I found another workaround so I decided to share it, hopefully this solves it for someone else. Took me two hours to figure it out....
iTunes: 11.1.3.8
Device: iPhone 4, iOS 7.0.4
Problem: Recently Restored my iPhone. After updating iTunes and the iPhone, I could no longer drag and drop playlists onto the iPhone. I have the sidebar activated, but this somehow disables the "iPhone button" and "Add to" options listed above, couldn't find these ANYWHERE. Whenever I copied a playlist directly to the iPhone (drag and drop onto the iPhone logo under Devices) it would create a playlist, with all the songs 'waiting to copy'. iTunes would then proceed to do f*** all and never actually copy the files onto the device. When I did manage to copy a playlist (do not ask me how, I don't remember), the playlist didn't show up on the iPhone and I ended up adding all the songs (which did copy) to a playlist manually on the iPhone. It's a special **** reserved only for stubborn Apple users apparently....
Solution: The ONLY thing that has worked for me so far is the following. Create a new Playlist on the iPhone manually (this is again so counter-intuitive that I am surprised people even use this Apple crap at all). To do this select the iPhone under Devices and then go to the Menu Bar (activated by pressing Ctrl+B on a Windows PC). Select File->New->Playlist. This creates a blank Playlist on your iPhone. You can then drag and drop individual songs to this playlist. They are copied to the iPhone and when you open your Music app, lo and behold, it actually recognises the playlist! And it plays the songs! Glory hallelujah!
Of course, as stated above, you need to have your iPhone set up so you can Manually manage music and turn off all wi-fi syncing, iTunes Match and any other such crap, for this to work. You also need to have the Sidebar showing.
So it's not true drag and drop, but it's better than nothing. At least I can put music on my iPhone again.
Thanks Apple, for making ubiquitous products which are impossible to use without a degree in Astrophysics!
Hope this helps someone